Extreme gravity tests with gravitational waves from compact binary coalescences: (I) inspiral–merger

Emanuele Berti; Kent Yagi; Nicolás Yunes

doi:10.1007/s10714-018-2362-8

General Relativity and Gravitation

April 2018, 50:46 | Cite as

Extreme gravity tests with gravitational waves from compact binary coalescences: (I) inspiral–merger

Authors
Authors and affiliations

Emanuele Berti
Kent Yagi
Nicolás Yunes

Editor’s Choice (Review Article)

First Online: 03 April 2018

Received: 15 January 2018

Accepted: 05 March 2018

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Part of the following topical collections:

Testing the Kerr spacetime with gravitational-wave and electromagnetic observations

Abstract

The observation of the inspiral and merger of compact binaries by the LIGO/Virgo collaboration ushered in a new era in the study of strong-field gravity. We review current and future tests of strong gravity and of the Kerr paradigm with gravitational-wave interferometers, both within a theory-agnostic framework (the parametrized post-Einsteinian formalism) and in the context of specific modified theories of gravity (scalar–tensor, Einstein–dilaton–Gauss–Bonnet, dynamical Chern–Simons, Lorentz-violating, and extra dimensional theories). In this contribution we focus on (i) the information carried by the inspiral radiation, and (ii) recent progress in numerical simulations of compact binary mergers in modified gravity.

Keywords

Modified gravity Gravitational waves Compact binary systems

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Notes

Acknowledgements

E.B. was supported by NSF Grants Nos. PHY-1607130 and AST-1716715. N.Y. acknowledges support through the NSF CAREER Grant PHY-1250636 and NASA Grants NNX16AB98G and 80NSSC17M0041.

A: Derivation of the black hole scalar charge in decoupled dynamical Gauss–Bonnet gravity

The goal of this appendix is to derive the scalar charge in D$^2$GB gravity for a stationary black hole, valid to arbitrary order in spin. We closely follow the calculation in dCS gravity in [181]. The scalar charge $\mu $ can be read off from the 1 / r coefficient in the asymptotic behavior of the scalar field at spatial infinity as $\phi = \mu \, M/r + {\mathcal {O}}(M^2/r^2)$, where M is the black hole mass. Since we work within the small-coupling approximation, we can take the background metric to be Kerr, and the above equation becomes

$$\begin{aligned} \frac{\partial }{\partial {{\tilde{r}}}} \left( \varDelta \frac{\partial \phi }{\partial {{\tilde{r}}}} \right) + \frac{1}{\sin \theta } \frac{\partial }{\partial \theta } \left( \sin \theta \frac{\partial \phi }{\partial \theta } \right) =T\,, \end{aligned}$$

(23)

where we work in the rescaled radial coordinate ${{\tilde{r}}} \equiv r/M$ and $\varDelta \equiv {{\tilde{r}}}^2 - 2M {{\tilde{r}}} + \chi ^2$ with $\chi $ representing the dimensionless Kerr parameter, and

$$\begin{aligned} T\equiv & {} - 48 \frac{\alpha _\mathrm{GB}\, M^2}{\Sigma ^5} \left[ {{\tilde{r}}}^6 -15 {{\tilde{r}}}^4 \chi ^2 \cos ^2 \theta +15 {{\tilde{r}}}^2 \chi ^4 \cos ^4 \theta - \chi ^6 \cos ^6 \theta \right] \,, \end{aligned}$$

(24)

with $\Sigma \equiv {{\tilde{r}}}^2 + \chi ^2 \cos ^2\theta $.

In order to solve the above field equation using Green’s functions, we decompose the scalar field $\phi $ and the source term T as [312]

$$\begin{aligned} \phi= & {} \frac{\alpha _\mathrm{GB}}{M^2} \sum _{\ell } R_{\ell }({{\tilde{r}}})\, S_{\ell }(\theta )\,, \end{aligned}$$

(25)

$$\begin{aligned} T= & {} \frac{\alpha _\mathrm{GB}}{M^2} \sum _{\ell } T_{\ell }({{\tilde{r}}})\, S_{\ell }(\theta )\,, \end{aligned}$$

(26)

where $S_\ell (\theta )$ is normalized as

$$\begin{aligned} 2 \pi \int _0^\pi S_\ell ^2\, \sin \theta \, d\theta = 1\,. \end{aligned}$$

(27)

Inverting Eq. (26), one obtains

$$\begin{aligned} T_\ell = 2 \pi \frac{M^2}{\alpha _\mathrm{GB}} \int _{0}^{\pi } T\, S_{\ell }\, \sin \theta \, d\theta \,. \end{aligned}$$

(28)

Eq. (23) can be split into radial and angular parts as

$$\begin{aligned} \frac{\partial }{\partial {{\tilde{r}}}} \left( \varDelta \frac{\partial R_{\ell }}{\partial {{\tilde{r}}}} \right) -\ell (\ell +1) R_{\ell }= & {} T_{\ell }\,, \end{aligned}$$

(29)

$$\begin{aligned} \frac{1}{\sin \theta } \frac{\partial }{\partial \theta } \left( \sin \theta \frac{\partial S_{\ell }}{\partial \theta } \right) + \ell (\ell +1) S_{\ell }= & {} 0\,. \end{aligned}$$

(30)

The solution to the second equation is nothing but the $m=0$ mode of the spherical harmonics $S_{\ell } = Y_{\ell 0}$.

Let us first derive the scalar monopole charge by concentrating on the $\ell = 0$ mode. The solution to Eq. (29) consists of homogeneous and particular solutions. Let us first study the former. Modulo overall integration constants, homogeneous solutions for the $\ell = 0$ mode of Eq. (29) are given by

$$\begin{aligned} R_0^{(\mathrm {hom},1)} ({{\tilde{r}}})= & {} 1, \end{aligned}$$

(31)

$$\begin{aligned} R_0^{(\mathrm {hom},2)} ({{\tilde{r}}})= & {} \frac{1}{2 \sqrt{1-\chi ^2}} \log \left( \frac{{{\tilde{r}}}-1-\sqrt{1-\chi ^2}}{{{\tilde{r}}}-1 + \sqrt{1-\chi ^2}}\right) . \end{aligned}$$

(32)

The asymptotic behavior of $R_0^{(\mathrm {hom},2)}$ at spatial infinity and at the Kerr horizon ${\tilde{r}}_\mathrm {hor} \equiv 1 + \sqrt{1-\chi ^2}$ is given by

$$\begin{aligned} R_0^{(\mathrm {hom},2,\mathrm {inf})} ({{\tilde{r}}})= & {} \frac{1}{{\tilde{r}}} + {\mathcal {O}}\left( \frac{1}{{\tilde{r}}^{2}} \right) , \end{aligned}$$

(33)

$$\begin{aligned} R_0^{(\mathrm {hom},2,\mathrm {hor})} ({{\tilde{r}}})= & {} \frac{1}{2 \sqrt{1-\chi ^2}} \log \left( \frac{{\tilde{r}}-{\tilde{r}}_\mathrm {hor}}{2\sqrt{1-\chi ^2}} \right) + {\mathcal {O}}[({\tilde{r}}-{\tilde{r}}_\mathrm {hor})]. \end{aligned}$$

(34)

Since EdGB gravity is a shift-symmetric theory, one can set $\phi (\infty ) = 0$ without loss of generality (namely no contribution from $R_0^{(\mathrm {hom},1)}$). Imposing further regularity at the horizon, one finds that the homogeneous solution is absent.

Let us now turn our attention to the particular solution $R_0^{(\mathrm {p})} ({{\tilde{r}}})$. Such a solution is obtained by using the Green’s function constructed from the two independent homogeneous solutions above [313, 314, 315]:

$$\begin{aligned} R_0^{(\mathrm {p})} ({{\tilde{r}}})= & {} \frac{1}{\varDelta \; W} \left[ R_0^{(\mathrm {hom},2)} ({{\tilde{r}}}) \int _{{{\tilde{r}}}_\mathrm {hor}}^{{{\tilde{r}}}} T_0({{\tilde{r}}}')\, R_0^{(\mathrm {hom},1)} ({{\tilde{r}}}')\, d{{\tilde{r}}}' \right. \nonumber \\&\left. - R_0^{(\mathrm {hom},1)} ({{\tilde{r}}}) \int _\infty ^{{{\tilde{r}}}} T_0 ({{\tilde{r}}}') \,R_0^{(\mathrm {hom},2)} ({{\tilde{r}}}') \, d{{\tilde{r}}}' \right] \,, \end{aligned}$$

(35)

where W is the Wronskian:

$$\begin{aligned} W \equiv R_0^{(\mathrm {hom},1)}\, \frac{d}{d{{\tilde{r}}}} R_0^{(\mathrm {hom},2)} - R_0^{(\mathrm {hom},2)}\, \frac{d}{d{{\tilde{r}}}} R_0^{(\mathrm {hom},1)} = \frac{1}{\varDelta }\,. \end{aligned}$$

(36)

The lower bound of the integral in Eq. (35) is determined such that the solution is regular at the horizon and satisfies $\phi (\infty ) = 0$. For the purpose of studying the leading asymptotic behavior at infinity, one only needs to consider the first term in Eq. (35).

Combining Eqs. (25) and (35) and performing the integral in the latter, one reads off the monopole scalar charge as

$$\begin{aligned} \mu ^\mathrm{GB}= & {} \frac{\alpha _\mathrm{GB}}{M^2} \frac{Y_{00}}{\varDelta \; W} \int _{{{\tilde{r}}}_\mathrm {hor}}^\infty T_0({{\tilde{r}}}')\, R_0^{(\mathrm {hom},1)} ({{\tilde{r}}}')\, d{{\tilde{r}}}' \nonumber \\= & {} 4 \frac{\alpha _\mathrm{GB}}{M^2} \frac{\sqrt{1-\chi ^2}-1 + \chi ^2}{\chi ^2}\,. \end{aligned}$$

(37)

We checked that when we expand the above scalar charge around $\chi = 0$, the expression agrees with that in [81] to ${\mathcal {O}}(\chi ^8)$.

In a similar manner, one can calculate the quadrupolar scalar charge $q^\mathrm{GB}$ by extracting the coefficient of $P_2(\cos \theta ) M^3/r^3$ in the asymptotic behavior of the scalar field at spatial infinity. One finds

$$\begin{aligned} q^\mathrm{GB}= & {} -\frac{4}{3 \chi ^3} \frac{\alpha }{M^2} \left\{ \chi \left[ 2 \chi ^2 \left( \chi ^2+\sqrt{1-\chi ^2}-2\right) -5 \sqrt{1-\chi ^2}+8\right] \right. \nonumber \\&\left. \quad +6 \tan ^{-1}\left( \frac{\sqrt{1-\chi ^2}-1}{\chi }\right) \right\} . \end{aligned}$$

(38)

Again, we checked that an expansion of this expression about $\chi =0$ agrees with that in [81] to ${\mathcal {O}}(\chi ^8)$.

B: A “dynamical no-hair theorem” for black holes in scalar–tensor gravity

The goal of this appendix is to show and explain how black hole binaries do not develop scalar hair upon dynamical evolution. That is, we will explain how the dynamics of a black hole binary system in Bergmann–Wagoner theory with vanishing potential in asymptotically flat spacetimes are the same as in GR, focusing first on the inspiral phase of coalescence.

In the inspiral phase of the binary’s evolution it is appropriate to use the PN approximation, an expansion in powers of $v/c \sim (Gm/rc^2)^{1/2}$. It is convenient to introduce a rescaled version of the scalar field $\phi $: $\varphi \equiv \phi /\phi _0$, where $\phi _0$ is the value of $\phi $ at infinity (assumed to be constant). Mirshekari and Will [191] found the equations of motion for the bodies up to 2.5PN order. Schematically, the relative acceleration ${\mathbf {a}} \equiv {\mathbf {a}}_1-{\mathbf {a}}_2$ takes the form

$$\begin{aligned} a^i =&-\frac{G\alpha m}{r^2}{\hat{n}}^i+\frac{G\alpha m}{r^2}(A_\text {PN}{\hat{n}}^i+B_\text {PN}{\dot{r}}v^i)+\frac{8}{5}\eta \frac{(G\alpha m)^2}{r^3}(A_\text {1.5PN}{\dot{r}}{\hat{n}}^i-B_\text {1.5PN}v^i) \nonumber \\&{}+\frac{G\alpha m}{r^2}(A_\text {2PN}{\hat{n}}^i+B_\text {2PN}{\dot{r}}v^i) \, , \end{aligned}$$

(39)

where $m \equiv m_1+m_2$, $\eta \equiv m_1m_2/m^2$, r is the orbital separation, ${\hat{\mathbf {n}}}$ is a unit vector pointing from body 2 to body 1, and ${\mathbf {v}} \equiv {\mathbf {v}}_1-{\mathbf {v}}_2$ is the relative velocity. The coefficients $A_\text {PN}$, $B_\text {PN}$, $A_\text {1.5PN}$, $B_\text {1.5PN}$, $A_\text {2PN}$, and $B_\text {2PN}$ (which are typically time-dependent) are given in [191]. The symbol G represents the combination $(4+2\omega _0)/[\phi _0(3+2\omega _0)]$ [with $\omega _0 \equiv \omega (\phi _0)$], which appears in the metric component $g_{00}$ in the same manner as the gravitational constant G in GR. However, the coupling in the Newtonian piece of the equations of motion is not simply G but $G\alpha $, where

$$\begin{aligned} \alpha \equiv \frac{3+2\omega _0}{4+2\omega _0}+\frac{(1-2s_1)(1-2s_2)}{4+2\omega _0} \, \end{aligned}$$

(40)

and $s_i$ ($i=1\,,2$) are the sensitivities of the two objects:

$$\begin{aligned} s_A \equiv \left( \frac{d\ln M_{\scriptscriptstyle A}(\phi )}{d\ln \phi }\right) _{\phi =\phi _0} \,. \end{aligned}$$

(41)

Higher-order derivatives of $M_{\scriptscriptstyle A}(\phi )$ are used to define higher-order sensitivities, e.g. $s'_{\scriptscriptstyle A}$ and $s''_{\scriptscriptstyle A}$. Note that in GR radiation reaction begins at 2.5PN order (quadrupole radiation), while in scalar–tensor gravity radiation reaction begins at 1.5PN order, due to the presence of dipole radiation.

All deviations from GR can be characterized using a fairly small number of parameters, all combinations of $\phi _0$, the Taylor coefficients of $\omega (\phi )$, and the sensitivities $s_A$, $s_A'$, and $s_A''$. If one object in the system is a black hole (with the other being a neutron star), the motion of the system is indistinguishable from GR up to 1PN order. All deviations beyond 1PN order depend only on a single parameter, which is a function of $\omega _0$ and the neutron star sensitivity. Unfortunately, this parameter alone (if measured) could not be used to distinguish between Brans–Dicke theory and a more general scalar–tensor theory.

Going beyond the equations of motion, the next step is the calculation of gravitational radiation. The tensor part of the radiation, encoded in ${\tilde{h}}^{ij}$, was computed up to 2PN order by Lang [192]. All deviations depend on the same (small) number of parameters that characterize the equations of motion. For black hole-neutron star systems, the waveform is indistinguishable from GR up to 1PN order, and deviations at higher order depend only on the single parameter described above. For binary black hole systems, the waveform is completely indistinguishable from GR. Scalar radiation has recently been computed by Lang [193] using a very similar procedure. The dipole moment generates the lowest-order scalar waves, which are of $-0.5$PN order:

$$\begin{aligned} \varphi = \frac{4G\mu \alpha ^{1/2}}{R}\zeta {\mathcal {S}}_-({\hat{\mathbf {N}}}\cdot {\mathbf {v}}), \end{aligned}$$

(42)

where $\mu \equiv m_1 m_2/m$ is the reduced mass, ${\hat{\mathbf {N}}} \equiv {\mathbf {x}}/R$ is the direction from the source to the detector, $\zeta \equiv 1/(4+2\omega _0)$, and

$$\begin{aligned} {\mathcal {S}}_- \equiv \alpha ^{-1/2}(s_2-s_1). \end{aligned}$$

(43)

Because computing the radiation up to 2PN order requires knowledge of the monopole moment to 3PN order (relative to itself) and knowledge of the dipole moment to 2.5PN order, Lang [193] computed the scalar waveform only to 1.5PN order. The 1.5PN waveform is described by the same set of parameters that describes the 2.5PN equations of motion and the 2PN tensor waveform. Again, the scalar waveform vanishes for binary black hole systems (so that the GW signal is indistinguishable from GR).

Lang [193] used the tensor and scalar waveforms to compute the total energy flux carried off to infinity to 1PN order. A derivation of the quadrupole-order flux in tensor-multiscalar theories (that agrees with Lang’s results in the single-scalar limit) can be found in [12]. A similar calculation for compact binaries in the massive Brans–Dicke theory was performed by Alsing et al. [52] (see also [316, 317]). In the notation used above, and correcting a mistake in [52], they found that the lowest-order flux is given by

$$\begin{aligned} {\dot{E}} = \frac{4}{3}\frac{\mu \eta }{r}\left( \frac{G\alpha m}{r}\right) ^3\zeta {\mathcal {S}}_-^2\left[ \frac{\omega ^2-m_s^2}{\omega ^2}\right] ^{3/2}\varTheta (\omega -m_s), \end{aligned}$$

(44)

where $\omega $ is the binary’s orbital frequency, $m_s$ is the mass of the scalar field, and $\varTheta $ is the Heaviside function (i.e., in massive Brans–Dicke theory, scalar dipole radiation is emitted only when $\omega > m_s$).

The emitted radiation has very special features for a binary black hole system: from Eq. (40) and (42) with $s_1=s_2=1/2$ we see that the dominant terms are identical to the equations of motion in GR, except for an unobservable mass rescaling. This result is a generalization to binary systems of “no-scalar-hair” theorems that apply to single black holes [318]. For generic mass ratio, Mirshekari and Will proved this “generalized no-hair theorem” up to 2.5PN order, but they conjectured that it should hold at all PN orders. Indeed, Ref. [277] has shown that the equations of motion are the same as in GR at any PN order if one considers an extreme mass-ratio system and works to lowest order in the mass ratio, and the conjecture is also supported by numerical relativity studies [287, 288]. This “generalized no-hair theorem” for binary black holes depends on some crucial assumptions: vanishing scalar potential, asymptotically constant value of the scalar field, and vanishing matter content. If any one of these assumptions breaks down, the black hole binary’s behavior will differ from GR.

References

1.
Sakharov, A.D.: Pisma. Zh. Eksp. Teor. Fiz. 5, 32 (1967). https://doi.org/10.1070/PU1991v034n05ABEH002497. [Usp. Fiz. Nauk 161, 61 (1991)]CrossRefGoogle Scholar
2.
Alexander, S.H.S., Gates, J., James, S.: JCAP 0606, 018 (2006). arXiv:hep-th/0409014 ADSCrossRefGoogle Scholar
3.
Alexander, S., Yunes, N.: Phys. Rep. 480, 1 (2009). https://doi.org/10.1016/j.physrep.2009.07.002. arXiv:0907.2562 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
4.
Pilo, L.: PoS EPS-HEP2011, 076 (2011)Google Scholar
5.
Paulos, M.F., Tolley, A.J.: JHEP 09, 002 (2012). https://doi.org/10.1007/JHEP09(2012)002. arXiv:1203.4268 [hep-th]ADSCrossRefGoogle Scholar
6.
Will, C.M.: Living Rev. Relativ. 17, 4 (2014). https://doi.org/10.12942/lrr-2014-4. arXiv:1403.7377 [gr-qc]ADSCrossRefGoogle Scholar
7.
Stairs, I.H.: Living Rev. Relativ. 6, 5 (2003). https://doi.org/10.12942/lrr-2003-5. arXiv:astro-ph/0307536 [astro-ph]ADSCrossRefGoogle Scholar
8.
Brans, C., Dicke, R.H.: Phys. Rev. 124, 925 (1961). https://doi.org/10.1103/PhysRev.124.925 ADSMathSciNetCrossRefGoogle Scholar
9.
Fierz, M.: Helv. Phys. Acta 29, 128 (1956)MathSciNetGoogle Scholar
10.
Jordan, P.: Z. Phys. 157, 112 (1959). https://doi.org/10.1007/BF01375155 ADSCrossRefGoogle Scholar
11.
Bertotti, B., Iess, L., Tortora, P.: Nature 425, 374 (2003). https://doi.org/10.1038/nature01997 ADSCrossRefGoogle Scholar
12.
Damour, T., Esposito-Farese, G.: Class. Quantum Gravity 9, 2093 (1992). https://doi.org/10.1088/0264-9381/9/9/015 ADSCrossRefGoogle Scholar
13.
Damour, T., Esposito-Farese, G.: Phys. Rev. Lett. 70, 2220 (1993). https://doi.org/10.1103/PhysRevLett.70.2220 ADSCrossRefGoogle Scholar
14.
Damour, T., Esposito-Farese, G.: Phys. Rev. D 54, 1474 (1996). https://doi.org/10.1103/PhysRevD.54.1474. arXiv:gr-qc/9602056 [gr-qc]ADSCrossRefGoogle Scholar
15.
Damour, T., Nordtvedt, K.: Phys. Rev. Lett. 70, 2217 (1993). https://doi.org/10.1103/PhysRevLett.70.2217 ADSCrossRefGoogle Scholar
16.
Damour, T., Nordtvedt, K.: Phys. Rev. D 48, 3436 (1993). https://doi.org/10.1103/PhysRevD.48.3436 ADSMathSciNetCrossRefGoogle Scholar
17.
Sampson, L., Yunes, N., Cornish, N., Ponce, M., Barausse, E., Klein, A., Palenzuela, C., Lehner, L.: Phys. Rev. D 90(12), 124091 (2014). https://doi.org/10.1103/PhysRevD.90.124091. arXiv:1407.7038 [gr-qc]ADSCrossRefGoogle Scholar
18.
Anderson, D., Yunes, N., Barausse, E.: Phys. Rev. D 94(10), 104064 (2016). https://doi.org/10.1103/PhysRevD.94.104064. arXiv:1607.08888 [gr-qc]ADSCrossRefGoogle Scholar
19.
Yunes, N., Pretorius, F.: Phys. Rev. D 79, 084043 (2009). https://doi.org/10.1103/PhysRevD.79.084043. arXiv:0902.4669 [gr-qc]ADSCrossRefGoogle Scholar
20.
Yunes, N., Stein, L.C.: Phys. Rev. D 83, 104002 (2011). https://doi.org/10.1103/PhysRevD.83.104002. arXiv:1101.2921 [gr-qc]ADSCrossRefGoogle Scholar
21.
Ali-Haimoud, Y.: Phys. Rev. D 83, 124050 (2011). arXiv:1105.0009 [astro-ph.HE]ADSCrossRefGoogle Scholar
22.
Ali-Haimoud, Y., Chen, Y.: Phys. Rev. D 84, 124033 (2011). https://doi.org/10.1103/PhysRevD.84.124033. arXiv:1110.5329 [astro-ph.HE]ADSCrossRefGoogle Scholar
23.
Yagi, K., Stein, L.C., Yunes, N., Tanaka, T.: Phys. Rev. D 85, 064022 (2012). https://doi.org/10.1103/PhysRevD.85.064022. arXiv:1110.5950 [gr-qc]ADSCrossRefGoogle Scholar
24.
Yagi, K., Stein, L.C., Yunes, N.: Phys. Rev. D 93(2), 024010 (2016). https://doi.org/10.1103/PhysRevD.93.024010. arXiv:1510.02152 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
25.
Kocsis, B., Yunes, N., Loeb, A. (2011). arXiv:1104.2322 [astro-ph.GA]
26.
Yunes, N., Kocsis, B., Loeb, A., Haiman, Z: (2011). arXiv:1103.4609 [astro-ph.CO]
27.
Hayasaki, K., Yagi, K., Tanaka, T., Mineshige, S.: Phys. Rev. D 87(4), 044051 (2013). https://doi.org/10.1103/PhysRevD.87.044051. arXiv:1201.2858 [astro-ph.CO]ADSCrossRefGoogle Scholar
28.
Barausse, E., Cardoso, V., Pani, P.: Phys. Rev. D 89(10), 104059 (2014). https://doi.org/10.1103/PhysRevD.89.104059. arXiv:1404.7149 [gr-qc]ADSCrossRefGoogle Scholar
29.
Abbott, B.P., et al.: Phys. Rev. Lett. 116(6), 061102 (2016). https://doi.org/10.1103/PhysRevLett.116.061102. arXiv:1602.03837 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
30.
Abbott, B.P., et al.: Phys. Rev. Lett. 116(24), 241103 (2016). https://doi.org/10.1103/PhysRevLett.116.241103. arXiv:1606.04855 [gr-qc]ADSCrossRefGoogle Scholar
31.
Abbott, B.P., et al.: Phys. Rev. Lett. 118(22), 221101 (2017). https://doi.org/10.1103/PhysRevLett.118.221101. arXiv:1706.01812 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
32.
Abbott, B.P., et al.: Phys. Rev. Lett. 119(14), 141101 (2017). https://doi.org/10.1103/PhysRevLett.119.141101. arXiv:1709.09660 [gr-qc]ADSCrossRefGoogle Scholar
33.
Abbott, B.P., et al.: Phys. Rev. Lett. 119, 161101 (2017). https://doi.org/10.1103/PhysRevLett.119.161101. arXiv:1710.05832 [gr-qc]ADSCrossRefGoogle Scholar
34.
Abbott, B.P., et al.: (2017). arXiv:1711.05578 [astro-ph.HE]
35.
Audley, H., et al.: (2017). arXiv:1702.00786 [astro-ph.IM]
36.
Yunes, N., Yagi, K., Pretorius, F.: Phys. Rev. D 94(8), 084002 (2016). https://doi.org/10.1103/PhysRevD.94.084002. arXiv:1603.08955 [gr-qc]ADSCrossRefGoogle Scholar
37.
Polchinski, J.: String Theory. Vol. 1: An Introduction to the Bosonic String. Cambridge University Press, Cambridge (2007)zbMATHGoogle Scholar
38.
Duff, M.J.: in The Oskar Klein centenary. In: Proceedings, symposium, Stockholm, Sweden, September 19–21, 1994, pp. 22–35 (1994)Google Scholar
39.
Randall, L., Sundrum, R.: Phys. Rev. Lett. 83, 3370 (1999). https://doi.org/10.1103/PhysRevLett.83.3370. arXiv:hep-ph/9905221 [hep-ph]ADSMathSciNetCrossRefGoogle Scholar
40.
Randall, L., Sundrum, R.: Phys. Rev. Lett. 83, 4690 (1999). https://doi.org/10.1103/PhysRevLett.83.4690. arXiv:hep-th/9906064 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
41.
Clifton, T., Ferreira, P.G., Padilla, A., Skordis, C.: Phys. Rep. 513, 1 (2012). https://doi.org/10.1016/j.physrep.2012.01.001. arXiv:1106.2476 [astro-ph.CO]ADSMathSciNetCrossRefGoogle Scholar
42.
Chiba, T., Harada, T., Nakao, K.I.: Prog. Theor. Phys. Suppl. 128, 335 (1997). https://doi.org/10.1143/PTPS.128.335 ADSCrossRefGoogle Scholar
43.
Fujii, Y., Maeda, K.I.: The Scalar-Tensor Theory of Gravitation. Cambridge University Press (2007)Google Scholar
44.
Faraoni, V.: Cosmology in Scalar Tensor Gravity. Springer (2011)Google Scholar
45.
Sotiriou, T.P.: Lect. Notes Phys. 892, 3 (2015). https://doi.org/10.1007/978-3-319-10070-8_1. arXiv:1404.2955 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
46.
Berti, E., et al.: Class. Quantum Gravity 32, 243001 (2015). https://doi.org/10.1088/0264-9381/32/24/243001. arXiv:1501.07274 [gr-qc]ADSCrossRefGoogle Scholar
47.
Bergmann, P.G.: Int. J. Theor. Phys. 1, 25 (1968). https://doi.org/10.1007/BF00668828 CrossRefGoogle Scholar
48.
Wagoner, R.V.: Phys. Rev. D 1, 3209 (1970). https://doi.org/10.1103/PhysRevD.1.3209 ADSCrossRefGoogle Scholar
49.
Horbatsch, M., Silva, H.O., Gerosa, D., Pani, P., Berti, E., Gualtieri, L., Sperhake, U.: Class. Quantum Gravity 32(20), 204001 (2015). https://doi.org/10.1088/0264-9381/32/20/204001. arXiv:1505.07462 [gr-qc]ADSCrossRefGoogle Scholar
50.
Flanagan, E.E.: Class. Quantum Gravity 21, 3817 (2004). https://doi.org/10.1088/0264-9381/21/15/N02. arXiv:gr-qc/0403063 [gr-qc]ADSCrossRefGoogle Scholar
51.
Sotiriou, T.P., Faraoni, V., Liberati, S.: Int. J. Mod. Phys. D 17, 399 (2008). https://doi.org/10.1142/S0218271808012097. arXiv:0707.2748 [gr-qc]ADSCrossRefGoogle Scholar
52.
Alsing, J., Berti, E., Will, C.M., Zaglauer, H.: Phys. Rev. D 85, 064041 (2012). https://doi.org/10.1103/PhysRevD.85.064041. arXiv:1112.4903 [gr-qc]ADSCrossRefGoogle Scholar
53.
Damour, T., Esposito-Farese, G.: Phys. Rev. D 53, 5541 (1996). https://doi.org/10.1103/PhysRevD.53.5541. arXiv:gr-qc/9506063 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
54.
Freire, P.C.C., Wex, N., Esposito-Farese, G., Verbiest, J.P.W., Bailes, M., Jacoby, B.A., Kramer, M., Stairs, I.H., Antoniadis, J., Janssen, G.H.: Mon. Not. R. Astron. Soc. 423, 3328 (2012). https://doi.org/10.1111/j.1365-2966.2012.21253.x. arXiv:1205.1450 ADSCrossRefGoogle Scholar
55.
Shao, L., Sennett, N., Buonanno, A., Kramer, M., Wex, N.: Phys. Rev. X 7(4), 041025 (2017). https://doi.org/10.1103/PhysRevX.7.041025. arXiv:1704.07561 [gr-qc]CrossRefGoogle Scholar
56.
Horndeski, G.W.: Int. J. Theor. Phys. 10, 363 (1974). https://doi.org/10.1007/BF01807638 CrossRefGoogle Scholar
57.
Deffayet, C., Gao, X., Steer, D.A., Zahariade, G.: Phys. Rev. D 84, 064039 (2011). https://doi.org/10.1103/PhysRevD.84.064039. arXiv:1103.3260 [hep-th]ADSCrossRefGoogle Scholar
58.
Kobayashi, T., Yamaguchi, M., Yokoyama, J.: Prog. Theor. Phys. 126, 511 (2011). https://doi.org/10.1143/PTP.126.511. arXiv:1105.5723 [hep-th]ADSCrossRefGoogle Scholar
59.
Maselli, A., Silva, H.O., Minamitsuji, M., Berti, E.: Phys. Rev. D 92(10), 104049 (2015). https://doi.org/10.1103/PhysRevD.92.104049. arXiv:1508.03044 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
60.
Langlois, D., Noui, K.: JCAP 1607(07), 016 (2016). https://doi.org/10.1088/1475-7516/2016/07/016. arXiv:1512.06820 [gr-qc]ADSCrossRefGoogle Scholar
61.
Langlois, D.: In 52nd Rencontres de Moriond on Gravitation (Moriond Gravitation 2017) La Thuile, Italy, March 25–April 1, 2017, pp. 221–228. https://inspirehep.net/record/1609629/files/arXiv:1707.03625.pdf (2017)
62.
Heisenberg, L.: JCAP 1405, 015 (2014). https://doi.org/10.1088/1475-7516/2014/05/015. arXiv:1402.7026 [hep-th]ADSCrossRefGoogle Scholar
63.
Heisenberg, L., Kase, R., Tsujikawa, S.: Phys. Lett. B 760, 617 (2016). https://doi.org/10.1016/j.physletb.2016.07.052. arXiv:1605.05565 [hep-th]ADSCrossRefGoogle Scholar
64.
Maeda, Ki, Ohta, N., Sasagawa, Y.: Phys. Rev. D80, 104032 (2009). https://doi.org/10.1103/PhysRevD.80.104032. arXiv:0908.4151 [hep-th]ADSCrossRefGoogle Scholar
65.
Yagi, K.: Phys. Rev. D 86, 081504 (2012). https://doi.org/10.1103/PhysRevD.86.081504. arXiv:1204.4524 [gr-qc]ADSCrossRefGoogle Scholar
66.
Pani, P., Cardoso, V.: Phys. Rev. D 79, 084031 (2009). https://doi.org/10.1103/PhysRevD.79.084031. arXiv:0902.1569 [gr-qc]ADSCrossRefGoogle Scholar
67.
Pani, P., Berti, E., Cardoso, V., Read, J.: Phys. Rev. D 84, 104035 (2011). https://doi.org/10.1103/PhysRevD.84.104035. arXiv:1109.0928 [gr-qc]ADSCrossRefGoogle Scholar
68.
Kanti, P., Mavromatos, N., Rizos, J., Tamvakis, K., Winstanley, E.: Phys. Rev. D 54, 5049 (1996). https://doi.org/10.1103/PhysRevD.54.5049. arXiv:hep-th/9511071 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
69.
Torii, T., Yajima, H., Maeda, Ki: Phys. Rev. D 55, 739 (1997). https://doi.org/10.1103/PhysRevD.55.739. arXiv:gr-qc/9606034 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
70.
Alexeev, S.O., Pomazanov, M.V.: Phys. Rev. D 55, 2110 (1997). https://doi.org/10.1103/PhysRevD.55.2110. arXiv:hep-th/9605106 [hep-th]ADSCrossRefGoogle Scholar
71.
Kleihaus, B., Kunz, J., Radu, E.: Phys. Rev. Lett. 106, 151104 (2011). https://doi.org/10.1103/PhysRevLett.106.151104. arXiv:1101.2868 [gr-qc]ADSCrossRefGoogle Scholar
72.
Kleihaus, B., Kunz, J., Mojica, S.: Phys. Rev. D 90(6), 061501 (2014). https://doi.org/10.1103/PhysRevD.90.061501. arXiv:1407.6884 [gr-qc]ADSCrossRefGoogle Scholar
73.
Kokkotas, K.D., Konoplya, R.A., Zhidenko, A.: Phys. Rev. D 96(6), 064004 (2017). https://doi.org/10.1103/PhysRevD.96.064004. arXiv:1706.07460 [gr-qc]ADSCrossRefGoogle Scholar
74.
Deffayet, C., Deser, S., Esposito-Farese, G.: Phys. Rev. D 80, 064015 (2009). https://doi.org/10.1103/PhysRevD.80.064015. arXiv:0906.1967 [gr-qc]ADSCrossRefGoogle Scholar
75.
Crisostomi, M., Noui, K., Charmousis, C., Langlois, D: (2017). arXiv:1710.04531 [hep-th]
76.
Papallo, G.: (2017). arXiv:1710.10155 [gr-qc]
77.
Mignemi, S., Stewart, N.R.: Phys. Rev. D 47, 5259 (1993). https://doi.org/10.1103/PhysRevD.47.5259. arXiv:hep-th/9212146 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
78.
Mignemi, S.: Phys. Rev. D 51, 934 (1995). https://doi.org/10.1103/PhysRevD.51.934. arXiv:hep-th/9303102 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
79.
Sotiriou, T.P., Zhou, S.Y.: Phys. Rev. D 90, 124063 (2014). https://doi.org/10.1103/PhysRevD.90.124063. arXiv:1408.1698 [gr-qc]ADSCrossRefGoogle Scholar
80.
Pani, P., Macedo, C.F.B., Crispino, L.C.B., Cardoso, V.: Phys. Rev. D 84, 087501 (2011). https://doi.org/10.1103/PhysRevD.84.087501. arXiv:1109.3996 [gr-qc]ADSCrossRefGoogle Scholar
81.
Ayzenberg, D., Yunes, N.: Phys. Rev. D 90, 044066 (2014). https://doi.org/10.1103/PhysRevD.91.069905,10.1103/PhysRevD.90.044066. Erratum: Phys. Rev. D91, no.6, 069905 (2015). arXiv:1405.2133 [gr-qc]ADSCrossRefGoogle Scholar
82.
Maselli, A., Pani, P., Gualtieri, L., Ferrari, V.: Phys. Rev. D 92(8), 083014 (2015). https://doi.org/10.1103/PhysRevD.92.083014. arXiv:1507.00680 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
83.
Will, C.M., Zaglauer, H.W.: Astrophys. J. 346, 366 (1989). https://doi.org/10.1086/168016 ADSCrossRefGoogle Scholar
84.
Alty, L.J.: J. Math. Phys. 36, 3094 (1995). https://doi.org/10.1063/1.531015 ADSMathSciNetCrossRefGoogle Scholar
85.
Gilkey, P., Park, J.H.: J. Geom. Phys. 88, 88 (2014). https://doi.org/10.1016/j.geomphys.2014.11.006 ADSCrossRefGoogle Scholar
86.
Benkel, R., Sotiriou, T.P., Witek, H.: Class. Quantum Gravity 34(6), 064001 (2017). https://doi.org/10.1088/1361-6382/aa5ce7. arXiv:1610.09168 [gr-qc]ADSCrossRefGoogle Scholar
87.
Benkel, R., Sotiriou, T.P., Witek, H.: Phys. Rev. D 94(12), 121503 (2016). https://doi.org/10.1103/PhysRevD.94.121503. arXiv:1612.08184 [gr-qc]ADSCrossRefGoogle Scholar
88.
Barausse, E., Yagi, K.: Phys. Rev. Lett. 115(21), 211105 (2015). https://doi.org/10.1103/PhysRevLett.115.211105. arXiv:1509.04539 [gr-qc]ADSCrossRefGoogle Scholar
89.
Barausse, E.: In: Proceedings, 3rd International Symposium on Quest for the Origin of Particles and the Universe (KMI2017): Nagoya, Japan, January 5–7, 2017. https://inspirehep.net/record/1517771/files/arXiv:1703.05699.pdf (2017)
90.
Lehebel, A., Babichev, E., Charmousis, C.: JCAP 1707(07), 037 (2017). https://doi.org/10.1088/1475-7516/2017/07/037. arXiv:1706.04989 [gr-qc]ADSCrossRefGoogle Scholar
91.
Silva, H.O., Sakstein, J., Gualtieri, L., Sotiriou, T.P., Berti, E.: (2017). arXiv:1711.02080 [gr-qc]
92.
Doneva, D.D., Yazadjiev, S.S.: (2017). arXiv:1712.03715 [gr-qc]
93.
Antoniou, G., Bakopoulos, A., Kanti, P.: (2017). arXiv:1711.03390 [hep-th]
94.
Antoniou, G., Bakopoulos, A., Kanti, P.: (2017). arXiv:1711.07431 [hep-th]
95.
Taveras, V., Yunes, N.: Phys. Rev. D 78, 064070 (2008). https://doi.org/10.1103/PhysRevD.78.064070. arXiv:0807.2652 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
96.
Calcagni, G., Mercuri, S.: (2009). arXiv:0902.0957 [gr-qc]
97.
Weinberg, S.: Phys. Rev. D 77, 123541 (2008). https://doi.org/10.1103/PhysRevD.77.123541. arXiv:0804.4291 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
98.
Delsate, T., Hilditch, D., Witek, H.: Phys. Rev. D 91(2), 024027 (2015). https://doi.org/10.1103/PhysRevD.91.024027. arXiv:1407.6727 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
99.
Konno, K., Matsuyama, T., Tanda, S.: Prog. Theor. Phys. 122, 561 (2009). https://doi.org/10.1143/PTP.122.561. arXiv:0902.4767 [gr-qc]ADSCrossRefGoogle Scholar
100.
Yagi, K., Yunes, N., Tanaka, T.: Phys. Rev. D 86, 044037 (2012). https://doi.org/10.1103/PhysRevD.89.049902,10.1103/PhysRevD.86.044037. Erratum: Phys. Rev. D89, 049902 (2014). arXiv:1206.6130 [gr-qc]ADSCrossRefGoogle Scholar
101.
Stein, L.C.: Phys. Rev. D 90(4), 044061 (2014). https://doi.org/10.1103/PhysRevD.90.044061. arXiv:1407.2350 [gr-qc]ADSCrossRefGoogle Scholar
102.
McNees, R., Stein, L.C., Yunes, N.: Class. Quantum Gravity 33(23), 235013 (2016). https://doi.org/10.1088/0264-9381/33/23/235013. arXiv:1512.05453 [gr-qc]ADSCrossRefGoogle Scholar
103.
Jackiw, R., Pi, S.Y.: Phys. Rev. D 68, 104012 (2003). https://doi.org/10.1103/PhysRevD.68.104012. arXiv:gr-qc/0308071 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
104.
Yunes, N., Sopuerta, C.F.: Phys. Rev. D 77, 064007 (2008). https://doi.org/10.1103/PhysRevD.77.064007. arXiv:0712.1028 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
105.
Grumiller, D., Yunes, N.: Phys. Rev. D 77, 044015 (2008). https://doi.org/10.1103/PhysRevD.77.044015. arXiv:0711.1868 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
106.
Ali-Haimoud, Y., Chen, Y.: Phys. Rev. D 84, 124033 (2011). arXiv:1110.5329 [astro-ph.HE]ADSCrossRefGoogle Scholar
107.
Yagi, K., Stein, L., Yunes, N., Tanaka, T.: Phys. Rev. D 87, 084058 (2013). https://doi.org/10.1103/PhysRevD.87.084058. arXiv:1302.1918 [gr-qc]ADSCrossRefGoogle Scholar
108.
Horava, P.: Phys. Rev. D 79, 084008 (2009). https://doi.org/10.1103/PhysRevD.79.084008. arXiv:0901.3775 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
109.
Wang, A.: Int. J. Mod. Phys. D 26(07), 1730014 (2017). https://doi.org/10.1142/S0218271817300142. arXiv:1701.06087 [gr-qc]ADSCrossRefGoogle Scholar
110.
Kostelecky, V.A.: Phys. Rev. D 69, 105009 (2004). arxiv:hep-th/0312310 [hep-th]ADSCrossRefGoogle Scholar
111.
Kostelecky, V.A., Russell, N.: Rev. Mod. Phys. 83, 11 (2011). https://doi.org/10.1103/RevModPhys.83.11. arXiv:0801.0287 [hep-ph]ADSCrossRefGoogle Scholar
112.
Mattingly, D.: Living Rev. Rel. 8, 5 (2005). arxiv:gr-qc/0502097 [gr-qc]CrossRefGoogle Scholar
113.
Jacobson, T., Liberati, S., Mattingly, D.: Ann. Phys. 321, 150 (2006). https://doi.org/10.1016/j.aop.2005.06.004. arXiv:astro-ph/0505267 [astro-ph]ADSCrossRefGoogle Scholar
114.
Colladay, D., Kostelecky, V.A.: Phys. Rev. D 58, 116002 (1998). https://doi.org/10.1103/PhysRevD.58.116002. arXiv:hep-ph/9809521 [hep-ph]ADSCrossRefGoogle Scholar
115.
Kostelecky, V.A.: (1998). arXiv:hep-ph/9810239 [hep-ph]
116.
Kostelecky, V.A.: (1999), pp. 151–163. arXiv:hep-ph/9912528 [hep-ph]
117.
Kostelecky, A.V., Tasson, J.D.: Phys. Rev. D 83, 016013 (2011). https://doi.org/10.1103/PhysRevD.83.016013. arXiv:1006.4106 [gr-qc]ADSCrossRefGoogle Scholar
118.
Liberati, S.: Class. Quantum Gravity 30, 133001 (2013). https://doi.org/10.1088/0264-9381/30/13/133001. arXiv:1304.5795 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
119.
Pospelov, M., Shang, Y.: Phys. Rev. D 85, 105001 (2012). https://doi.org/10.1103/PhysRevD.85.105001. arXiv:1010.5249 [hep-th]ADSCrossRefGoogle Scholar
120.
Bailey, Q.G., Kostelecky, V.A.: Phys. Rev. D 74, 045001 (2006). https://doi.org/10.1103/PhysRevD.74.045001. arXiv:gr-qc/0603030 [gr-qc]ADSCrossRefGoogle Scholar
121.
Bailey, Q.G.: Phys. Rev. D 80, 044004 (2009). https://doi.org/10.1103/PhysRevD.80.044004. arXiv:0904.0278 [gr-qc]ADSCrossRefGoogle Scholar
122.
Bailey, Q.G., Everett, R.D., Overduin, J.M.: (2013). arXiv:1309.6399 [hep-ph]
123.
Jacobson, T., Mattingly, D.: Phys. Rev. D 64, 024028 (2001). https://doi.org/10.1103/PhysRevD.64.024028. arXiv:gr-qc/0007031 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
124.
Jacobson, T.: PoS QG-PH, 020. (2007). arXiv:0801.1547 [gr-qc]
125.
Blas, D., Pujolas, O., Sibiryakov, S.: Phys. Rev. Lett. 104, 181302 (2010). https://doi.org/10.1103/PhysRevLett.104.181302. arXiv:0909.3525 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
126.
Yagi, K., Blas, D., Yunes, N., Barausse, E.: Phys. Rev. Lett. 112(16), 161101 (2014). https://doi.org/10.1103/PhysRevLett.112.161101. arXiv:1307.6219 [gr-qc]ADSCrossRefGoogle Scholar
127.
Yagi, K., Blas, D., Barausse, E., Yunes, N.: Phys. Rev. D 89, 084067 (2014). https://doi.org/10.1103/PhysRevD.89.084067. arXiv:1311.7144 [gr-qc]ADSCrossRefGoogle Scholar
128.
Abbott, B.P., et al.: Astrophys. J. 848(2), L13 (2017). https://doi.org/10.3847/2041-8213/aa920c. arXiv:1710.05834 [astro-ph.HE]ADSCrossRefGoogle Scholar
129.
Jacobson, T., Mattingly, D.: Phys. Rev. D 70, 024003 (2004). https://doi.org/10.1103/PhysRevD.70.024003. arXiv:gr-qc/0402005 [gr-qc]ADSCrossRefGoogle Scholar
130.
Foster, B.Z., Jacobson, T.: Phys. Rev. D 73, 064015 (2006). https://doi.org/10.1103/PhysRevD.73.064015. arXiv:gr-qc/0509083 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
131.
Foster, B.Z.: Phys. Rev. D 73, 104012 (2006). https://doi.org/10.1103/PhysRevD.75.129904,10.1103/PhysRevD.73.104012. arXiv:gr-qc/0602004 [gr-qc]ADSCrossRefGoogle Scholar
132.
Foster, B.Z.: Phys. Rev. D 76, 084033 (2007). https://doi.org/10.1103/PhysRevD.76.084033. arXiv:0706.0704 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
133.
Blas, D., Pujolas, O., Sibiryakov, S.: JHEP 1104, 018 (2011). https://doi.org/10.1007/JHEP04(2011)018. arXiv:1007.3503 [hep-th]ADSCrossRefGoogle Scholar
134.
Audren, B., Blas, D., Lesgourgues, J., Sibiryakov, S.: JCAP 1308, 039 (2013). https://doi.org/10.1088/1475-7516/2013/08/039. arXiv:1305.0009 [astro-ph.CO]ADSCrossRefGoogle Scholar
135.
Gumrukcuoglu, A.E., Saravani, M., Sotiriou, T.P.: (2017). arXiv:1711.08845 [gr-qc]
136.
Blas, D., Sanctuary, H.: Phys. Rev. D 84, 064004 (2011). https://doi.org/10.1103/PhysRevD.84.064004. arXiv:1105.5149 [gr-qc]ADSCrossRefGoogle Scholar
137.
Arkani-Hamed, N., Dimopoulos, S., Dvali, G.R.: Phys. Lett. B 429, 263 (1998). https://doi.org/10.1016/S0370-2693(98)00466-3. arXiv:hep-ph/9803315 [hep-ph]ADSCrossRefGoogle Scholar
138.
Arkani-Hamed, N., Dimopoulos, S., Dvali, G.R.: Phys. Rev. D 59, 086004 (1999). https://doi.org/10.1103/PhysRevD.59.086004. arXiv:hep-ph/9807344 [hep-ph]ADSCrossRefGoogle Scholar
139.
Garriga, J., Tanaka, T.: Phys. Rev. Lett. 84, 2778 (2000). https://doi.org/10.1103/PhysRevLett.84.2778. arXiv:hep-th/9911055 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
140.
Adelberger, E.G., Heckel, B.R., Hoedl, S.A., Hoyle, C.D., Kapner, D.J., Upadhye, A.: Phys. Rev. Lett. 98, 131104 (2007). https://doi.org/10.1103/PhysRevLett.98.131104. arXiv:hep-ph/0611223 [hep-ph]ADSCrossRefGoogle Scholar
141.
Maldacena, J.M.: Int. J. Theor. Phys. 38, 1113 (1999). https://doi.org/10.1023/A:1026654312961. Adv. Theor. Math. Phys. 2, 231 (1998). arXiv:hep-th/9711200 [hep-th]MathSciNetCrossRefGoogle Scholar
142.
Aharony, O., Gubser, S.S., Maldacena, J.M., Ooguri, H., Oz, Y.: Phys. Rep. 323, 183 (2000). https://doi.org/10.1016/S0370-1573(99)00083-6. arXiv:hep-th/9905111 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
143.
Emparan, R., Fabbri, A., Kaloper, N.: JHEP 08, 043 (2002). arXiv:hep-th/0206155 [hep-th]ADSCrossRefGoogle Scholar
144.
Tanaka, T.: Prog. Theor. Phys. Suppl. 148, 307 (2003). https://doi.org/10.1143/PTPS.148.307. arXiv:gr-qc/0203082 [gr-qc]ADSCrossRefGoogle Scholar
145.
Emparan, R., Garcia-Bellido, J., Kaloper, N.: JHEP 01, 079 (2003). https://doi.org/10.1088/1126-6708/2003/01/079. arXiv:hep-th/0212132 [hep-th]ADSCrossRefGoogle Scholar
146.
Figueras, P., Wiseman, T.: Phys. Rev. Lett. 107, 081101 (2011). https://doi.org/10.1103/PhysRevLett.107.081101. arXiv:1105.2558 [hep-th]ADSCrossRefGoogle Scholar
147.
Abdolrahimi, S., Cattoen, C., Page, D.N., Yaghoobpour-Tari, S.: Phys. Lett. B 720, 405 (2013). https://doi.org/10.1016/j.physletb.2013.02.034. arXiv:1206.0708 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
148.
Babichev, E., Dokuchaev, V., Eroshenko, Y.: Phys. Rev. Lett. 93, 021102 (2004). https://doi.org/10.1103/PhysRevLett.93.021102. arXiv:gr-qc/0402089 [gr-qc]ADSCrossRefGoogle Scholar
149.
Babichev, E., Dokuchaev, V., Eroshenko, Y.: J. Exp. Theor. Phys. 100, 528 (2005). https://doi.org/10.1134/1.1901765. Zh. Eksp. Teor. Fiz. 127, 597(2005). arXiv:astroph/0505618 [astro-ph]ADSCrossRefGoogle Scholar
150.
Babichev, E.O., Dokuchaev, V.I., Eroshenko, Y.N.: Phys. Usp. 56, 1155 (2013). https://doi.org/10.3367/UFNr.0183.201312a.1257,10.3367/UFNe.0183.201312a.1257. Usp. Fiz. Nauk 189, no.12, 1257 (2013). arXiv:1406.0841 [gr-qc]ADSCrossRefGoogle Scholar
151.
Yunes, N., Pretorius, F., Spergel, D.: Phys. Rev. D 81, 064018 (2010). https://doi.org/10.1103/PhysRevD.81.064018. arXiv:0912.2724 [gr-qc]ADSCrossRefGoogle Scholar
152.
Nordtvedt, K.: Phys. Rev. 169, 1017 (1968)ADSCrossRefGoogle Scholar
153.
Will, C.M.: APJ 163, 611 (1971)ADSCrossRefGoogle Scholar
154.
Will, C.M., Nordtvedt, K.J.: APJ 177, 757 (1972)ADSCrossRefGoogle Scholar
155.
Nordtvedt, K.J., Will, C.M.: APJ 177, 775 (1972)ADSCrossRefGoogle Scholar
156.
Arun, K.G., Iyer, B.R., Qusailah, M.S.S., Sathyaprakash, B.S.: Class. Quantum Gravity 23, L37 (2006). https://doi.org/10.1088/0264-9381/23/9/L01. arXiv:gr-qc/0604018 [gr-qc]ADSCrossRefGoogle Scholar
157.
Arun, K.G., Iyer, B.R., Qusailah, M.S.S., Sathyaprakash, B.S.: Phys. Rev. D 74, 024006 (2006). https://doi.org/10.1103/PhysRevD.74.024006. arXiv:gr-qc/0604067 [gr-qc]ADSCrossRefGoogle Scholar
158.
Mishra, C.K., Arun, K.G., Iyer, B.R., Sathyaprakash, B.S.: Phys. Rev. D 82, 064010 (2010). https://doi.org/10.1103/PhysRevD.82.064010. arXiv:1005.0304 [gr-qc]ADSCrossRefGoogle Scholar
159.
Damour, T., Taylor, J.H.: Phys. Rev. D 45, 1840 (1992). https://doi.org/10.1103/PhysRevD.45.1840 ADSCrossRefGoogle Scholar
160.
Alexander, S., Finn, L.S., Yunes, N.: Phys. Rev. D 78, 066005 (2008). https://doi.org/10.1103/PhysRevD.78.066005. arXiv:0712.2542 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
161.
Yunes, N., O’Shaughnessy, R., Owen, B.J., Alexander, S.: Phys. Rev. D 82, 064017 (2010). https://doi.org/10.1103/PhysRevD.82.064017. arXiv:1005.3310 [gr-qc]ADSCrossRefGoogle Scholar
162.
Yagi, K., Yang, H.: (2017). arXiv:1712.00682 [gr-qc]
163.
Husa, S., Khan, S., Hannam, M., Purrer, M., Ohme, F., Forteza, X.J., Bohe, A.: Phys. Rev. D 93, 044006 (2016). https://doi.org/10.1103/PhysRevD.93.044006. Phys. Rev. D93, 044006 (2016). arXiv:1508.07250 [gr-qc]ADSCrossRefGoogle Scholar
164.
Khan, S., Husa, S., Hannam, M., Ohme, F., Purrer, M., Forteza, X.J., Bohe, A.: Phys. Rev. D 93, 044007 (2016). https://doi.org/10.1103/PhysRevD.93.044007. Phys. Rev. D 93, 044007 (2016). arXiv:1508.07253 [gr-qc]ADSCrossRefGoogle Scholar
165.
Yunes, N., Pretorius, F.: Phys. Rev. D 80, 122003 (2009). https://doi.org/10.1103/PhysRevD.80.122003. arXiv:0909.3328 [gr-qc]ADSCrossRefGoogle Scholar
166.
Cornish, N., Sampson, L., Yunes, N., Pretorius, F.: Phys. Rev. D 84, 062003 (2011). https://doi.org/10.1103/PhysRevD.84.062003. arXiv:1105.2088 [gr-qc]ADSCrossRefGoogle Scholar
167.
Chatziioannou, K., Yunes, N., Cornish, N.: Phys. Rev. D 86, 022004 (2012). https://doi.org/10.1103/PhysRevD.86.022004. arXiv:1204.2585 [gr-qc]ADSCrossRefGoogle Scholar
168.
Sampson, L., Cornish, N., Yunes, N.: Phys. Rev. D 89(6), 064037 (2014). https://doi.org/10.1103/PhysRevD.89.064037. arXiv:1311.4898 [gr-qc]ADSCrossRefGoogle Scholar
169.
Sampson, L., Cornish, N., Yunes, N.: Phys. Rev. D 87(10), 102001 (2013). https://doi.org/10.1103/PhysRevD.87.102001. arXiv:1303.1185 [gr-qc]ADSCrossRefGoogle Scholar
170.
Vallisneri, M., Yunes, N.: Phys. Rev. D 87(10), 102002 (2013). https://doi.org/10.1103/PhysRevD.87.102002. arXiv:1301.2627 [gr-qc]ADSCrossRefGoogle Scholar
171.
Tso, R., Isi, M., Chen, Y., Stein, L.: In: Proceedings, 7th Meeting on CPT and Lorentz Symmetry (CPT 16): Bloomington, Indiana, USA, June 20–24, 2016, pp. 205–208. (2017). https://doi.org/10.1142/9789813148505_0052. https://inspirehep.net/record/1479158/files/arXiv:1608.01284.pdf
172.
Krishnendu, N.V., Arun, K.G., Mishra, C.K.: Phys. Rev. Lett. 119(9), 091101 (2017). https://doi.org/10.1103/PhysRevLett.119.091101. arXiv:1701.06318 [gr-qc]ADSCrossRefGoogle Scholar
173.
Chatziioannou, K., Cornish, N., Klein, A., Yunes, N.: Astrophys. J. 798(1), L17 (2015). https://doi.org/10.1088/2041-8205/798/1/L17. arXiv:1402.3581 [gr-qc]ADSCrossRefGoogle Scholar
174.
Chatziioannou, K., Cornish, N., Klein, A., Yunes, N.: Phys. Rev. D 89(10), 104023 (2014). https://doi.org/10.1103/PhysRevD.89.104023. arXiv:1404.3180 [gr-qc]ADSCrossRefGoogle Scholar
175.
Chatziioannou, K., Klein, A., Cornish, N., Yunes, N.: Phys. Rev. Lett. 118(5), 051101 (2017). https://doi.org/10.1103/PhysRevLett.118.051101. arXiv:1606.03117 [gr-qc]ADSCrossRefGoogle Scholar
176.
Chatziioannou, K., Klein, A., Yunes, N., Cornish, N.: Phys. Rev. D 95(10), 104004 (2017). https://doi.org/10.1103/PhysRevD.95.104004. arXiv:1703.03967 [gr-qc]ADSCrossRefGoogle Scholar
177.
Cardoso, V., Franzin, E., Maselli, A., Pani, P., Raposo, G.: Phys. Rev. D 95(8), 084014 (2017). https://doi.org/10.1103/PhysRevD.95.089901. Addendum: Phys. Rev. D 95, no.8, 089901 (2017). arXiv:1701.01116 [gr-qc]ADSCrossRefGoogle Scholar
178.
Maselli, A., Pani, P., Cardoso, V., Abdelsalhin, T., Gualtieri, L., Ferrari, V.: (2017). arXiv:1703.10612 [gr-qc]
179.
Jacobson, T.: Phys. Rev. Lett. 83, 2699 (1999). https://doi.org/10.1103/PhysRevLett.83.2699. arXiv:astro-ph/9905303 [astro-ph]ADSMathSciNetCrossRefGoogle Scholar
180.
Horbatsch, M.W., Burgess, C.P.: JCAP 1205, 010 (2012). https://doi.org/10.1088/1475-7516/2012/05/010. arXiv:1111.4009 [gr-qc]ADSCrossRefGoogle Scholar
181.
Yagi, K., Yunes, N., Tanaka, T.: Phys. Rev. Lett. 109, 251105 (2012). https://doi.org/10.1103/PhysRevLett.116.169902,10.1103/PhysRevLett.109.251105. Erratum: Phys. Rev. Lett. 116, no.16, 169902 (2016). arXiv:1208.5102 [gr-qc]ADSCrossRefGoogle Scholar
182.
Hansen, D., Yunes, N., Yagi, K.: Phys. Rev. D 91(8), 082003 (2015). https://doi.org/10.1103/PhysRevD.91.082003. arXiv:1412.4132 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
183.
Yagi, K., Tanahashi, N., Tanaka, T.: Phys. Rev. D 83, 084036 (2011). https://doi.org/10.1103/PhysRevD.83.084036. arXiv:1101.4997 [gr-qc]ADSCrossRefGoogle Scholar
184.
Mirshekari, S., Yunes, N., Will, C.M.: Phys. Rev. D 85, 024041 (2012). https://doi.org/10.1103/PhysRevD.85.024041. arXiv:1110.2720 [gr-qc]ADSCrossRefGoogle Scholar
185.
Eardley, D.M.: APJ 196, L59 (1975). https://doi.org/10.1086/181744 ADSCrossRefGoogle Scholar
186.
Will, C.M.: Astrophys. J. 214, 826 (1977). https://doi.org/10.1086/155313 ADSCrossRefGoogle Scholar
187.
Damour, T., Esposito-Farese, G.: Phys. Rev. D 58, 042001 (1998). https://doi.org/10.1103/PhysRevD.58.042001. arXiv:gr-qc/9803031 [gr-qc]ADSCrossRefGoogle Scholar
188.
Will, C.M., Wiseman, A.G.: Phys. Rev. D 54, 4813 (1996). https://doi.org/10.1103/PhysRevD.54.4813. arXiv:gr-qc/9608012 [gr-qc]ADSCrossRefGoogle Scholar
189.
Pati, M.E., Will, C.M.: Phys. Rev. D 62, 124015 (2000). https://doi.org/10.1103/PhysRevD.62.124015. arXiv:gr-qc/0007087 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
190.
Pati, M.E., Will, C.M.: Phys. Rev. D 65, 104008 (2002). https://doi.org/10.1103/PhysRevD.65.104008. arXiv:gr-qc/0201001 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
191.
Mirshekari, S., Will, C.M.: Phys. Rev. D 87(8), 084070 (2013). https://doi.org/10.1103/PhysRevD.87.084070. arXiv:1301.4680 [gr-qc]ADSCrossRefGoogle Scholar
192.
Lang, R.N.: Phys. Rev. D 89(8), 084014 (2014). https://doi.org/10.1103/PhysRevD.89.084014. arXiv:1310.3320 [gr-qc]ADSCrossRefGoogle Scholar
193.
Lang, R.N.: Phys. Rev. D 91(8), 084027 (2015). https://doi.org/10.1103/PhysRevD.91.084027. arXiv:1411.3073 [gr-qc]ADSCrossRefGoogle Scholar
194.
Sennett, N., Marsat, S., Buonanno, A.: Phys. Rev. D 94(8), 084003 (2016). https://doi.org/10.1103/PhysRevD.94.084003. arXiv:1607.01420 [gr-qc]ADSCrossRefGoogle Scholar
195.
Julié, F.L., Deruelle, N.: Phys. Rev. D 95(12), 124054 (2017). https://doi.org/10.1103/PhysRevD.95.124054. arXiv:1703.05360 [gr-qc]ADSCrossRefGoogle Scholar
196.
Julié, F.L.: (2017). arXiv:1709.09742 [gr-qc]
197.
Buonanno, A., Damour, T.: Phys. Rev. D 59, 084006 (1999). https://doi.org/10.1103/PhysRevD.59.084006. arXiv:gr-qc/9811091 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
198.
Will, C.M.: Phys. Rev. D 57, 2061 (1998). https://doi.org/10.1103/PhysRevD.57.2061. arXiv:gr-qc/9709011 [gr-qc]ADSCrossRefGoogle Scholar
199.
Rubakov, V.A., Tinyakov, P.G.: Phys. Usp. 51, 759 (2008). https://doi.org/10.1070/PU2008v051n08ABEH006600. arXiv:0802.4379 [hep-th]ADSCrossRefGoogle Scholar
200.
Hinterbichler, K.: Rev. Mod. Phys. 84, 671 (2012). https://doi.org/10.1103/RevModPhys.84.671. arXiv:1105.3735 [hep-th]ADSCrossRefGoogle Scholar
201.
de Rham, C.: Living Rev. Rel. 17, 7 (2014). https://doi.org/10.12942/lrr-2014-7. arXiv:1401.4173 [hep-th]CrossRefGoogle Scholar
202.
Calcagni, G.: Phys. Rev. Lett. 104, 251301 (2010). https://doi.org/10.1103/PhysRevLett.104.251301. arXiv:0912.3142 [hep-th]ADSCrossRefGoogle Scholar
203.
Calcagni, G.: Adv. Theor. Math. Phys. 16(2), 549 (2012). https://doi.org/10.4310/ATMP.2012.v16.n2.a5. arXiv:1106.5787 [hep-th]MathSciNetCrossRefGoogle Scholar
204.
Calcagni, G.: JHEP 01, 065 (2012). https://doi.org/10.1007/JHEP01(2012)065. arXiv:1107.5041 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
205.
Calcagni, G.: (2016). arXiv:1603.03046 [gr-qc]
206.
Amelino-Camelia, G.: Phys. Lett. B 510, 255 (2001). https://doi.org/10.1016/S0370-2693(01)00506-8. arXiv:hep-th/0012238 [hep-th]ADSCrossRefGoogle Scholar
207.
Magueijo, J., Smolin, L.: Phys. Rev. Lett. 88, 190403 (2002). https://doi.org/10.1103/PhysRevLett.88.190403. arXiv:hep-th/0112090 [hep-th]ADSCrossRefGoogle Scholar
208.
Amelino-Camelia, G.: Nature 418, 34 (2002). https://doi.org/10.1038/418034a. arXiv:gr-qc/0207049 [gr-qc]ADSCrossRefGoogle Scholar
209.
Amelino-Camelia, G.: Symmetry 2, 230 (2010). https://doi.org/10.3390/sym2010230. arXiv:1003.3942 [gr-qc]CrossRefGoogle Scholar
210.
Sefiedgar, A.S., Nozari, K., Sepangi, H.R.: Phys. Lett. B 696, 119 (2011). https://doi.org/10.1016/j.physletb.2010.11.067. arXiv:1012.1406 [gr-qc]ADSCrossRefGoogle Scholar
211.
Kostelecky, V.A., Mewes, M.: Phys. Lett. B 757, 510 (2016). https://doi.org/10.1016/j.physletb.2016.04.040. arXiv:1602.04782 [gr-qc]ADSCrossRefGoogle Scholar
212.
Horava, P.: JHEP 03, 020 (2009). https://doi.org/10.1088/1126-6708/2009/03/020. arXiv:0812.4287 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
213.
Vacaru, S.I.: Gen. Relativ. Gravit. 44, 1015 (2012). https://doi.org/10.1007/s10714-011-1324-1. arXiv:1010.5457 [math-ph]ADSCrossRefGoogle Scholar
214.
Abbott, B.P., et al.: Phys. Rev. Lett. 116(22), 221101 (2016). https://doi.org/10.1103/PhysRevLett.116.221101. arXiv:1602.03841 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
215.
Abbott, B.P., et al.: (2016). arXiv:1606.04856 [gr-qc]
216.
Yunes, N., Hughes, S.A.: Phys. Rev. D 82, 082002 (2010). https://doi.org/10.1103/PhysRevD.82.082002. arXiv:1007.1995 [gr-qc]ADSCrossRefGoogle Scholar
217.
Sampson, L., Yunes, N., Cornish, N.: Phys. Rev. D 88(6), 064056 (2013). https://doi.org/10.1103/PhysRevD.88.089902. Erratum: Phys. Rev. D 88, no.8, 089902 (2013). arXiv:1307.8144 [gr-qc]ADSCrossRefGoogle Scholar
218.
Amendola, L., Charmousis, C., Davis, S.C.: JCAP 0710, 004 (2007). https://doi.org/10.1088/1475-7516/2007/10/004. arXiv:0704.0175 [astro-ph]ADSCrossRefGoogle Scholar
219.
Johannsen, T., Psaltis, D., McClintock, J.E.: Astrophys. J. 691, 997 (2009). https://doi.org/10.1088/0004-637X/691/2/997. arXiv:0803.1835 [astro-ph]ADSCrossRefGoogle Scholar
220.
Johannsen, T.: Astron. Astrophys. 507, 617 (2009). https://doi.org/10.1051/0004-6361/200912803. arXiv:0812.0809 ADSCrossRefGoogle Scholar
221.
Psaltis, D.: Phys. Rev. Lett. 98, 181101 (2007). https://doi.org/10.1103/PhysRevLett.98.181101. arXiv:astro-ph/0612611 ADSMathSciNetCrossRefGoogle Scholar
222.
Gnedin, O.Y., Maccarone, T.J., Psaltis, D., Zepf, S.E.: Astrophys. J. 705, L168 (2009). https://doi.org/10.1088/0004-637X/705/2/L168. arXiv:0906.5351 [astro-ph.CO]ADSCrossRefGoogle Scholar
223.
Manchester, R.N.: Int. J. Mod. Phys. D 24(06), 1530018 (2015). https://doi.org/10.1142/S0218271815300189. arXiv:1502.05474 [gr-qc]ADSCrossRefGoogle Scholar
224.
Konopliv, A.S., Asmar, S.W., Folkner, W.M., Karatekin, Ö., Nunes, D.C., Smrekar, S.E., Yoder, C.F., Zuber, M.T.: Icarus 211, 401 (2011). https://doi.org/10.1016/j.icarus.2010.004 ADSCrossRefGoogle Scholar
225.
Hofmann, F., Müller, J., Biskupek, L.: Astron. Astrophys. 522, L5 (2010). https://doi.org/10.1051/0004-6361/201015659 ADSCrossRefGoogle Scholar
226.
Copi, C.J., Davis, A.N., Krauss, L.M.: Phys. Rev. Lett. 92, 171301 (2004). https://doi.org/10.1103/PhysRevLett.92.171301. arXiv:astro-ph/0311334 [astro-ph]ADSCrossRefGoogle Scholar
227.
Bambi, C., Giannotti, M., Villante, F.L.: Phys. Rev. D 71, 123524 (2005). https://doi.org/10.1103/PhysRevD.71.123524. arXiv:astro-ph/0503502 [astro-ph]ADSCrossRefGoogle Scholar
228.
Talmadge, C., Berthias, J.P., Hellings, R.W., Standish, E.M.: Phys. Rev. Lett. 61, 1159 (1988). https://doi.org/10.1103/PhysRevLett.61.1159 ADSCrossRefGoogle Scholar
229.
Finn, L.S., Sutton, P.J.: Phys. Rev. D 65, 044022 (2002). https://doi.org/10.1103/PhysRevD.65.044022. arXiv:gr-qc/0109049 ADSCrossRefGoogle Scholar
230.
Goldhaber, A.S., Nieto, M.M.: Phys. Rev. D 9, 1119 (1974). https://doi.org/10.1103/PhysRevD.9.1119 ADSCrossRefGoogle Scholar
231.
Hare, M.G.: Can. J. Phys. 51, 431 (1973). https://doi.org/10.1139/p73-056 ADSCrossRefGoogle Scholar
232.
Brito, R., Cardoso, V., Pani, P.: Phys. Rev. D 88(2), 023514 (2013). https://doi.org/10.1103/PhysRevD.88.023514. arXiv:1304.6725 [gr-qc]ADSCrossRefGoogle Scholar
233.
Kiyota, S., Yamamoto, K.: Phys. Rev. D 92(10), 104036 (2015). https://doi.org/10.1103/PhysRevD.92.104036. arXiv:1509.00610 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
234.
Blas, D., Ivanov, M.M., Sawicki, I., Sibiryakov, S.: Pisma Zh. Eksp. Teor. Fiz. 103(10), 708 (2016). https://doi.org/10.7868/S0370274X16100039. JETP Lett. 103, no.10, 624 (2016). arXiv:1602.04188 [gr-qc]CrossRefGoogle Scholar
235.
Cornish, N., Blas, D., Nardini, G.: (2017). arXiv:1707.06101 [gr-qc]
236.
Kobakhidze, A., Lagger, C., Manning, A.: Phys. Rev. D 94(6), 064033 (2016). https://doi.org/10.1103/PhysRevD.94.064033. arXiv:1607.03776 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
237.
Max, K., Platscher, M., Smirnov, J.: Phys. Rev. Lett. 119(11), 111101 (2017). https://doi.org/10.1103/PhysRevLett.119.111101. arXiv:1703.07785 [gr-qc]ADSCrossRefGoogle Scholar
238.
De Felice, A., Nakamura, T., Tanaka, T.: PTEP 2014, 043E01. (2014). https://doi.org/10.1093/ptep/ptu024. arXiv:1304.3920 [gr-qc]
239.
Gbm, F., et al.: Astrophys. J. 848, L12 (2017). https://doi.org/10.3847/2041-8213/aa91c9. arXiv:1710.05833 [astro-ph.HE]ADSCrossRefGoogle Scholar
240.
Boran, S., Desai, S., Kahya, E.O., Woodard, R.P.: (2017). arXiv:1710.06168 [astro-ph.HE]
241.
Shoemaker, I.M., Murase, K.: (2017). arXiv:1710.06427 [astro-ph.HE]
242.
Wang, H., et al.: (2017). arXiv:1710.05805 [astro-ph.HE]
243.
Wei, J.J., Fan, X.L., Zhang, B.B., Wu, X.F., Gao, H., Mészáros, P., Zhang, B., Dai, Z.G., Zhang, S.N., Zhu, Z.H.: (2017). arXiv:1710.05860 [astro-ph.HE]
244.
Lombriser, L., Taylor, A.: JCAP 1603(03), 031 (2016). https://doi.org/10.1088/1475-7516/2016/03/031. arXiv:1509.08458 [astro-ph.CO]ADSCrossRefGoogle Scholar
245.
Lombriser, L., Lima, N.A.: Phys. Lett. B 765, 382 (2017). https://doi.org/10.1016/j.physletb.2016.12.048. arXiv:1602.07670 [astro-ph.CO]ADSCrossRefGoogle Scholar
246.
Sakstein, J., Jain, B.: (2017). arXiv:1710.05893 [astro-ph.CO]
247.
Creminelli, P., Vernizzi, F.: (2017). arXiv:1710.05877 [astro-ph.CO]
248.
Ezquiaga, J.M., Zumalacárregui, M.: (2017). arXiv:1710.05901 [astro-ph.CO]
249.
Baker, T., Bellini, E., Ferreira, P.G., Lagos, M., Noller, J., Sawicki, I.: (2017). arXiv:1710.06394 [astro-ph.CO]
250.
Arai, S., Nishizawa, A.: (2017). arXiv:1711.03776 [gr-qc]
251.
Crisostomi, M., Koyama, K.: (2017). arXiv:1711.06661 [astro-ph.CO]
252.
Langlois, D., Saito, R., Yamauchi, D., Noui, K.: (2017). arXiv:1711.07403 [gr-qc]
253.
Dima, A., Vernizzi, F.: (2017). arXiv:1712.04731 [gr-qc]
254.
Visinelli, L., Bolis, N., Vagnozzi, S.: (2017). arXiv:1711.06628 [gr-qc]
255.
Nojiri, S., Odintsov, S.D.: (2017). arXiv:1711.00492 [astro-ph.CO]
256.
Lee, S.: (2017). arXiv:1711.09038 [gr-qc]
257.
Heisenberg, L., Tsujikawa, S.: (2017). arXiv:1711.09430 [gr-qc]
258.
Berti, E., Gair, J., Sesana, A.: Phys. Rev. D 84, 101501 (2011). https://doi.org/10.1103/PhysRevD.84.101501. arXiv:1107.3528 [gr-qc]ADSCrossRefGoogle Scholar
259.
Barausse, E., Yunes, N., Chamberlain, K.: Phys. Rev. Lett. 116(24), 241104 (2016). https://doi.org/10.1103/PhysRevLett.116.241104. arXiv:1603.04075 [gr-qc]ADSCrossRefGoogle Scholar
260.
Chamberlain, K., Yunes, N.: Phys. Rev. D 96(8), 084039 (2017). https://doi.org/10.1103/PhysRevD.96.084039. arXiv:1704.08268 [gr-qc]ADSCrossRefGoogle Scholar
261.
Samajdar, A., Arun, K.G.: (2017). arXiv:1708.00671 [gr-qc]
262.
Berti, E., Sesana, A., Barausse, E., Cardoso, V., Belczynski, K.: Phys. Rev. Lett. 117(10), 101102 (2016). https://doi.org/10.1103/PhysRevLett.117.101102. arXiv:1605.09286 [gr-qc]ADSCrossRefGoogle Scholar
263.
Okounkova, M., Stein, L.C., Scheel, M.A., Hemberger, D.A.: Phys. Rev. D 96(4), 044020 (2017). https://doi.org/10.1103/PhysRevD.96.044020. arXiv:1705.07924 [gr-qc]ADSCrossRefGoogle Scholar
264.
Papallo, G., Reall, H.S.: Phys. Rev. D 96(4), 044019 (2017). https://doi.org/10.1103/PhysRevD.96.044019. arXiv:1705.04370 [gr-qc]ADSCrossRefGoogle Scholar
265.
Cayuso, J., Ortiz, N., Lehner, L.: (2017). arXiv:1706.07421 [gr-qc]
266.
Lanahan-Tremblay, N., Faraoni, V.: Class. Quantum Gravity 24, 5667 (2007). https://doi.org/10.1088/0264-9381/24/22/024. arXiv:0709.4414 [gr-qc]ADSCrossRefGoogle Scholar
267.
Paschalidis, V., Halataei, S.M.H., Shapiro, S.L., Sawicki, I.: Class. Quantum Gravity 28, 085006 (2011). https://doi.org/10.1088/0264-9381/28/8/085006. arXiv:1103.0984 [gr-qc]ADSCrossRefGoogle Scholar
268.
Salgado, M., Martinez-del Rio, D., Alcubierre, M., Nunez, D.: Phys. Rev. D 77, 104010 (2008). https://doi.org/10.1103/PhysRevD.77.104010. arXiv:0801.2372 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
269.
Sotiriou, T.P., Zhou, S.Y.: Phys. Rev. Lett. 112, 251102 (2014). https://doi.org/10.1103/PhysRevLett.112.251102. arXiv:1312.3622 [gr-qc]ADSCrossRefGoogle Scholar
270.
Herdeiro, C.A.R., Radu, E.: Phys. Rev. Lett. 112, 221101 (2014). https://doi.org/10.1103/PhysRevLett.112.221101. arXiv:1403.2757 [gr-qc]ADSCrossRefGoogle Scholar
271.
Herdeiro, C., Radu, E.: Class. Quantum Gravity 32(14), 144001 (2015). https://doi.org/10.1088/0264-9381/32/14/144001. arXiv:1501.04319 [gr-qc]ADSCrossRefGoogle Scholar
272.
Herdeiro, C.A.R., Radu, E.: Int. J. Mod. Phys. D 24(09), 1542014 (2015). https://doi.org/10.1142/S0218271815420146. arXiv:1504.08209 [gr-qc]ADSCrossRefGoogle Scholar
273.
Ganchev, B., Santos, J.E.: (2017). arXiv:1711.08464 [gr-qc]
274.
Degollado, J.C., Herdeiro, C.A.R., Radu, E.: Gen. Relativ. Quantum Cosmol. (2018). arXiv:1802.07266 [gr-qc]
275.
Heusler, M.: Class. Quantum Gravity 12, 2021 (1995). https://doi.org/10.1088/0264-9381/12/8/017. arXiv:gr-qc/9503053 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
276.
Sotiriou, T.P., Faraoni, V.: Phys. Rev. Lett. 108, 081103 (2012). https://doi.org/10.1103/PhysRevLett.108.081103. arXiv:1109.6324 [gr-qc]ADSCrossRefGoogle Scholar
277.
Yunes, N., Pani, P., Cardoso, V.: Phys. Rev. D 85, 102003 (2012). https://doi.org/10.1103/PhysRevD.85.102003. arXiv:1112.3351 [gr-qc]ADSCrossRefGoogle Scholar
278.
Doneva, D.D., Yazadjiev, S.S.: (2017). arXiv:1711.01187 [gr-qc]
279.
Brito, R., Cardoso, V., Pani, P.: Lect. Notes Phys. 906, 1 (2015). https://doi.org/10.1007/978-3-319-19000-6. arXiv:1501.06570 [gr-qc]CrossRefGoogle Scholar
280.
Cardoso, V., Chakrabarti, S., Pani, P., Berti, E., Gualtieri, L.: Phys. Rev. Lett. 107, 241101 (2011). https://doi.org/10.1103/PhysRevLett.107.241101. arXiv:1109.6021 [gr-qc]ADSCrossRefGoogle Scholar
281.
Zimmerman, P.: Phys. Rev. D 92(6), 064051 (2015). https://doi.org/10.1103/PhysRevD.92.064051. arXiv:1507.04076 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
282.
Fujita, R., Cardoso, V.: Phys. Rev. D 95(4), 044016 (2017). https://doi.org/10.1103/PhysRevD.95.044016. arXiv:1612.00978 [gr-qc]ADSCrossRefGoogle Scholar
283.
Cardoso, V., Carucci, I.P., Pani, P., Sotiriou, T.P.: Phys. Rev. D 88, 044056 (2013). https://doi.org/10.1103/PhysRevD.88.044056. arXiv:1305.6936 [gr-qc]ADSCrossRefGoogle Scholar
284.
Cardoso, V., Carucci, I.P., Pani, P., Sotiriou, T.P.: Phys. Rev. Lett. 111, 111101 (2013). https://doi.org/10.1103/PhysRevLett.111.111101. arXiv:1308.6587 [gr-qc]ADSCrossRefGoogle Scholar
285.
Baumgarte, T.W., Shapiro, S.L.: Numerical Relativity: Solving Einstein’s Equations on the Computer. Cambridge University Press, Cambridge (2010). https://doi.org/10.1017/CBO9781139193344 zbMATHCrossRefGoogle Scholar
286.
Salgado, M.: Class. Quantum Gravity 23, 4719 (2006). https://doi.org/10.1088/0264-9381/23/14/010. arXiv:gr-qc/0509001 [gr-qc]ADSCrossRefGoogle Scholar
287.
Berti, E., Cardoso, V., Gualtieri, L., Horbatsch, M., Sperhake, U.: Phys. Rev. D 87(12), 124020 (2013). https://doi.org/10.1103/PhysRevD.87.124020. arXiv:1304.2836 [gr-qc]ADSCrossRefGoogle Scholar
288.
Healy, J., Bode, T., Haas, R., Pazos, E., Laguna, P., Shoemaker, D.M., Yunes, N.: Class. Quantum Gravity 29, 232002 (2012). https://doi.org/10.1088/0264-9381/29/23/232002. arXiv:1112.3928 [gr-qc]ADSCrossRefGoogle Scholar
289.
Sahni, V., Wang, L.M.: Phys. Rev. D 62, 103517 (2000). https://doi.org/10.1103/PhysRevD.62.103517. arXiv:astro-ph/9910097 [astro-ph]ADSCrossRefGoogle Scholar
290.
Hu, W., Barkana, R., Gruzinov, A.: Phys. Rev. Lett. 85, 1158 (2000). https://doi.org/10.1103/PhysRevLett.85.1158. arXiv:astro-ph/0003365 [astro-ph]ADSCrossRefGoogle Scholar
291.
Macedo, C.F.B., Pani, P., Cardoso, V., Crispino, L.C.B.: Astrophys. J. 774, 48 (2013). https://doi.org/10.1088/0004-637X/774/1/48. arXiv:1302.2646 [gr-qc]ADSCrossRefGoogle Scholar
292.
Nordtvedt, K.: Phys. Rev. 169, 1014 (1968). https://doi.org/10.1103/PhysRev.169.1014 ADSCrossRefGoogle Scholar
293.
Roll, P.G., Krotkov, R., Dicke, R.H.: Ann. Phys. 26, 442 (1964). https://doi.org/10.1016/0003-4916(64)90259-3 ADSCrossRefGoogle Scholar
294.
Shibata, M., Taniguchi, K., Okawa, H., Buonanno, A.: Phys. Rev. D 89(8), 084005 (2014). https://doi.org/10.1103/PhysRevD.89.084005. arXiv:1310.0627 [gr-qc]ADSCrossRefGoogle Scholar
295.
Silva, H.O., Macedo, C.F.B., Berti, E., Crispino, L.C.B.: Class. Quantum Gravity 32, 145008 (2015). https://doi.org/10.1088/0264-9381/32/14/145008. arXiv:1411.6286 [gr-qc]ADSCrossRefGoogle Scholar
296.
Barausse, E., Palenzuela, C., Ponce, M., Lehner, L.: Phys. Rev. D 87, 081506 (2013). https://doi.org/10.1103/PhysRevD.87.081506. arXiv:1212.5053 [gr-qc]ADSCrossRefGoogle Scholar
297.
Palenzuela, C., Barausse, E., Ponce, M., Lehner, L.: Phys. Rev. D 89(4), 044024 (2014). https://doi.org/10.1103/PhysRevD.89.044024. arXiv:1310.4481 [gr-qc]ADSCrossRefGoogle Scholar
298.
Sennett, N., Buonanno, A.: Phys. Rev. D 93(12), 124004 (2016). https://doi.org/10.1103/PhysRevD.93.124004. arXiv:1603.03300 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
299.
Mendes, R.F.P., Ortiz, N.: Phys. Rev. D 93(12), 124035 (2016). https://doi.org/10.1103/PhysRevD.93.124035. arXiv:1604.04175 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
300.
Palenzuela, C., Liebling, S.L.: Phys. Rev. D 93(4), 044009 (2016). https://doi.org/10.1103/PhysRevD.93.044009. arXiv:1510.03471 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
301.
Ponce, M., Palenzuela, C., Barausse, E., Lehner, L.: Phys. Rev. D 91(8), 084038 (2015). https://doi.org/10.1103/PhysRevD.91.084038. arXiv:1410.0638 [gr-qc]ADSCrossRefGoogle Scholar
302.
Sagunski, L., Zhang, J., Johnson, M.C., Lehner, L., Sakellariadou, M., Liebling, S.L., Palenzuela, C., Neilsen, D.: (2017). arXiv:1709.06634 [gr-qc]
303.
Jai-akson, P., Chatrabhuti, A., Evnin, O., Lehner, L.: Phys. Rev. D 96(4), 044031 (2017). https://doi.org/10.1103/PhysRevD.96.044031. arXiv:1706.06519 [gr-qc]ADSCrossRefGoogle Scholar
304.
Buonanno, A., Kidder, L.E., Lehner, L.: Phys. Rev. D 77, 026004 (2008). https://doi.org/10.1103/PhysRevD.77.026004. arXiv:0709.3839 [astro-ph]ADSCrossRefGoogle Scholar
305.
Hirschmann, E.W., Lehner, L., Liebling, S.L., Palenzuela, C.: (2017). arXiv:1706.09875 [gr-qc]
306.
Israel, W.: Ann. Phys. 100, 310 (1976). https://doi.org/10.1016/0003-4916(76)90064-6 ADSCrossRefGoogle Scholar
307.
Israel, W., Stewart, J.M.: Ann. Phys. 118, 341 (1979). https://doi.org/10.1016/0003-4916(79)90130-1 ADSCrossRefGoogle Scholar
308.
Endlich, S., Gorbenko, V., Huang, J., Senatore, L.: JHEP 09, 122 (2017). https://doi.org/10.1007/JHEP09(2017)122. arXiv:1704.01590 [gr-qc]ADSCrossRefGoogle Scholar
309.
Julié, F.L.: (2017). arXiv:1711.10769 [gr-qc]
310.
Glampedakis, K., Pappas, G., Silva, H.O., Berti, E.: Phys. Rev. D 96(6), 064054 (2017). https://doi.org/10.1103/PhysRevD.96.064054. arXiv:1706.07658 [gr-qc]ADSCrossRefGoogle Scholar
311.
Tattersall, O.J., Ferreira, P.G., Lagos, M.: (2017). arXiv:1711.01992 [gr-qc]
312.
Teukolsky, S.A.: Astrophys. J. 185, 635 (1973)ADSCrossRefGoogle Scholar
313.
Mino, Y., Sasaki, M., Shibata, M., Tagoshi, H., Tanaka, T.: Prog. Theor. Phys. Suppl. 128, 1 (1997). https://doi.org/10.1143/PTPS.128.1. arXiv:gr-qc/9712057 [gr-qc]ADSCrossRefGoogle Scholar
314.
Hughes, S.A.: Phys. Rev. D 61(8), 084004 (2000). https://doi.org/10.1103/PhysRevD.61.084004. Erratum: Phys. Rev. D90, no. 10, 109904 (2014). arXiv:gr-qc/9910091 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
315.
Sasaki, M., Tagoshi, H.: Living Rev. Rel. 6, 6 (2003). https://doi.org/10.12942/lrr-2003-6. arXiv:gr-qc/0306120 [gr-qc]CrossRefGoogle Scholar
316.
Krause, D., Kloor, H.T., Fischbach, E.: Phys. Rev. D 49, 6892 (1994). https://doi.org/10.1103/PhysRevD.49.6892 ADSCrossRefGoogle Scholar
317.
Perivolaropoulos, L.: Phys. Rev. D 81, 047501 (2010). https://doi.org/10.1103/PhysRevD.81.047501. arXiv:0911.3401 [gr-qc]ADSCrossRefGoogle Scholar
318.
Hawking, S.W.: Commun. Math. Phys. 25, 167 (1972). https://doi.org/10.1007/BF01877518 ADSCrossRefGoogle Scholar

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Emanuele Berti
- 1
Email authorView author's OrcID profile
Kent Yagi
- 2
Nicolás Yunes
- 3

1.Department of Physics and AstronomyThe University of MississippiUniversityUSA
2.Department of PhysicsUniversity of VirginiaCharlottesvilleUSA
3.Department of Physics, eXtreme Gravity InstituteMontana State UniversityBozemanUSA

Extreme gravity tests with gravitational waves from compact binary coalescences: (I) inspiral–merger

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