Abstract
Under the assumption that a UV theory does not display superluminal behavior, we ask what constraints on superluminality are satisfied in the effective field theory (EFT). We study two examples of effective theories: quantum electrodynamics (QED) coupled to gravity after the electron is integrated out, and the flat-space galileon. The first is realized in nature, the second is more speculative, but they both exhibit apparent superluminality around non-trivial backgrounds. In the QED case, we attempt, and fail, to find backgrounds for which the superluminal signal advance can be made larger than the putative resolving power of the EFT. In contrast, in the galileon case it is easy to find such backgrounds, indicating that if the UV completion of the galileon is (sub)luminal, quantum corrections must become important at distance scales of order the Vainshtein radius of the background configuration, much larger than the naive EFT strong coupling distance scale. Such corrections would be reminiscent of the non-perturbative Schwarzschild scale quantum effects that are expected to resolve the black hole information problem. Finally, a byproduct of our analysis is a calculation of how perturbative quantum effects alter charged Reissner-Nordstrom black holes.
Article PDF
References
E. Babichev, V. Mukhanov and A. Vikman, k-Essence, superluminal propagation, causality and emergent geometry, JHEP 02 (2008) 101 [arXiv:0708.0561] [INSPIRE].
R. Geroch, Faster Than Light?, AMS/IP Stud. Adv. Math. 49 (2011) 59 [arXiv:1005.1614] [INSPIRE].
C. Burrage, C. de Rham, L. Heisenberg and A.J. Tolley, Chronology Protection in Galileon Models and Massive Gravity, JCAP 07 (2012) 004 [arXiv:1111.5549] [INSPIRE].
G. Papallo and H.S. Reall, Graviton time delay and a speed limit for small black holes in Einstein-Gauss-Bonnet theory, JHEP 11 (2015) 109 [arXiv:1508.05303] [INSPIRE].
J. Friedman et al., Cauchy problem in space-times with closed timelike curves, Phys. Rev. D 42 (1990) 1915 [INSPIRE].
I.T. Drummond and S.J. Hathrell, QED Vacuum Polarization in a Background Gravitational Field and Its Effect on the Velocity of Photons, Phys. Rev. D 22 (1980) 343 [INSPIRE].
S. Dubovsky, A. Nicolis, E. Trincherini and G. Villadoro, Microcausality in curved space-time, Phys. Rev. D 77 (2008) 084016 [arXiv:0709.1483] [INSPIRE].
G.M. Shore, ‘Faster than light’ photons in gravitational fields: Causality, anomalies and horizons, Nucl. Phys. B 460 (1996) 379 [gr-qc/9504041] [INSPIRE].
G.M. Shore, Quantum gravitational optics, Contemp. Phys. 44 (2003) 503 [gr-qc/0304059] [INSPIRE].
G.M. Shore, Superluminality and UV completion, Nucl. Phys. B 778 (2007) 219 [hep-th/0701185] [INSPIRE].
I.B. Khriplovich, Superluminal velocity of photons in a gravitational background, Phys. Lett. B 346 (1995) 251 [gr-qc/9411052] [INSPIRE].
S. Mohanty and A.R. Prasanna, Photon propagation in Einstein and higher derivative gravity, Nucl. Phys. B 526 (1998) 501 [gr-qc/9804017] [INSPIRE].
G. Preti, A note on the geometrical-optics solution to the Maxwell tensor wave equation in curved spacetime, Nucl. Phys. B 834 (2010) 390 [INSPIRE].
R. Akhoury and A.D. Dolgov, On the Possibility of Super-luminal Propagation in a Gravitational Background, arXiv:1003.6110 [INSPIRE].
R.D. Daniels and G.M. Shore, ‘Faster than light’ photons and charged black holes, Nucl. Phys. B 425 (1994) 634 [hep-th/9310114] [INSPIRE].
R.D. Daniels and G.M. Shore, ‘Faster than light’ photons and rotating black holes, Phys. Lett. B 367 (1996) 75 [gr-qc/9508048] [INSPIRE].
T.J. Hollowood and G.M. Shore, Causality and Micro-Causality in Curved Spacetime, Phys. Lett. B 655 (2007) 67 [arXiv:0707.2302] [INSPIRE].
T.J. Hollowood and G.M. Shore, The refractive index of curved spacetime: The fate of causality in QED, Nucl. Phys. B 795 (2008) 138 [arXiv:0707.2303] [INSPIRE].
T.J. Hollowood and G.M. Shore, The Causal Structure of QED in Curved Spacetime: Analyticity and the Refractive Index, JHEP 12 (2008) 091 [arXiv:0806.1019] [INSPIRE].
T.J. Hollowood, G.M. Shore and R.J. Stanley, The Refractive Index of Curved Spacetime II: QED, Penrose Limits and Black Holes, JHEP 08 (2009) 089 [arXiv:0905.0771] [INSPIRE].
T.J. Hollowood and G.M. Shore, The Effect of Gravitational Tidal Forces on Vacuum Polarization: How to Undress a Photon, Phys. Lett. B 691 (2010) 279 [arXiv:1006.0145] [INSPIRE].
T.J. Hollowood and G.M. Shore, ‘Superluminal’ Photon Propagation in QED in Curved Spacetime is Dispersive and Causal, arXiv:1006.1238 [INSPIRE].
T.J. Hollowood and G.M. Shore, The Effect of Gravitational Tidal Forces on Renormalized Quantum Fields, JHEP 02 (2012) 120 [arXiv:1111.3174] [INSPIRE].
T.J. Hollowood and G.M. Shore, The Unbearable Beingness of Light, Dressing and Undressing Photons in Black Hole Spacetimes, Int. J. Mod. Phys. D 21 (2012) 1241003 [arXiv:1205.3291] [INSPIRE].
T.J. Hollowood and G.M. Shore, Causality Violation, Gravitational Shockwaves and UV Completion, JHEP 03 (2016) 129 [arXiv:1512.04952] [INSPIRE].
T.J. Hollowood and G.M. Shore, Causality, Renormalizability and Ultra-High Energy Gravitational Scattering, J. Phys. A 49 (2016) 215401 [arXiv:1601.06989] [INSPIRE].
J.Z. Simon, Higher Derivative Lagrangians, Nonlocality, Problems and Solutions, Phys. Rev. D 41 (1990) 3720 [INSPIRE].
X. Jaen, J. Llosa and A. Molina, A reduction of order two for infinite order lagrangians, Phys. Rev. D 34 (1986) 2302 [INSPIRE].
C.P. Burgess and M. Williams, Who You Gonna Call? Runaway Ghosts, Higher Derivatives and Time-Dependence in EFTs, JHEP 08 (2014) 074 [arXiv:1404.2236] [INSPIRE].
L. Brillouin, Wave Propagation and Group Velocity, Series in Pure & Applied Physics), Elsevier (1960).
P. Milonni, Fast Light, Slow Light and Left-Handed Light, Series in Optics and Optoelectronics, CRC Press (2004).
C. de Rham, Massive Gravity, Living Rev. Rel. 17 (2014) 7 [arXiv:1401.4173] [INSPIRE].
A. Nicolis, R. Rattazzi and E. Trincherini, The Galileon as a local modification of gravity, Phys. Rev. D 79 (2009) 064036 [arXiv:0811.2197] [INSPIRE].
G.R. Dvali, G. Gabadadze and M. Porrati, 4 – D gravity on a brane in 5 – D Minkowski space, Phys. Lett. B 485 (2000) 208 [hep-th/0005016] [INSPIRE].
M.A. Luty, M. Porrati and R. Rattazzi, Strong interactions and stability in the DGP model, JHEP 09 (2003) 029 [hep-th/0303116] [INSPIRE].
C. de Rham, G. Gabadadze and A.J. Tolley, Resummation of Massive Gravity, Phys. Rev. Lett. 106 (2011) 231101 [arXiv:1011.1232] [INSPIRE].
K. Hinterbichler, Theoretical Aspects of Massive Gravity, Rev. Mod. Phys. 84 (2012) 671 [arXiv:1105.3735] [INSPIRE].
C. de Rham, Galileons in the Sky, Comptes Rendus Physique 13 (2012) 666 [arXiv:1204.5492] [INSPIRE].
C. de Rham and A.J. Tolley, DBI and the Galileon reunited, JCAP 05 (2010) 015 [arXiv:1003.5917] [INSPIRE].
K. Hinterbichler, M. Trodden and D. Wesley, Multi-field galileons and higher co-dimension branes, Phys. Rev. D 82 (2010) 124018 [arXiv:1008.1305] [INSPIRE].
G. Goon, K. Hinterbichler and M. Trodden, Symmetries for Galileons and DBI scalars on curved space, JCAP 07 (2011) 017 [arXiv:1103.5745] [INSPIRE].
G. Goon, K. Hinterbichler and M. Trodden, A New Class of Effective Field Theories from Embedded Branes, Phys. Rev. Lett. 106 (2011) 231102 [arXiv:1103.6029] [INSPIRE].
A.I. Vainshtein, To the problem of nonvanishing gravitation mass, Phys. Lett. B 39 (1972) 393 [INSPIRE].
E. Babichev and C. Deffayet, An introduction to the Vainshtein mechanism, Class. Quant. Grav. 30 (2013) 184001 [arXiv:1304.7240] [INSPIRE].
G. Goon, K. Hinterbichler, A. Joyce and M. Trodden, Aspects of Galileon Non-Renormalization, JHEP 11 (2016) 100 [arXiv:1606.02295] [INSPIRE].
G. Goon, K. Hinterbichler and M. Trodden, Galileons on Cosmological Backgrounds, JCAP 12 (2011) 004 [arXiv:1109.3450] [INSPIRE].
M. Trodden and K. Hinterbichler, Generalizing Galileons, Class. Quant. Grav. 28 (2011) 204003 [arXiv:1104.2088] [INSPIRE].
G. Goon, K. Hinterbichler, A. Joyce and M. Trodden, Galileons as Wess-Zumino Terms, JHEP 06 (2012) 004 [arXiv:1203.3191] [INSPIRE].
G. Dvali, A. Gruzinov and M. Zaldarriaga, The accelerated universe and the moon, Phys. Rev. D 68 (2003) 024012 [hep-ph/0212069] [INSPIRE].
A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].
G.L. Goon, K. Hinterbichler and M. Trodden, Stability and superluminality of spherical DBI galileon solutions, Phys. Rev. D 83 (2011) 085015 [arXiv:1008.4580] [INSPIRE].
M. Andrews, K. Hinterbichler, J. Khoury and M. Trodden, Instabilities of Spherical Solutions with Multiple Galileons and SO(N) Symmetry, Phys. Rev. D 83 (2011) 044042 [arXiv:1008.4128] [INSPIRE].
J. Evslin and T. Qiu, Closed Timelike Curves in the Galileon Model, JHEP 11 (2011) 032 [arXiv:1106.0570] [INSPIRE].
T.L. Curtright and D.B. Fairlie, A Galileon Primer, arXiv:1212.6972 [INSPIRE].
P. de Fromont, C. de Rham, L. Heisenberg and A. Matas, Superluminality in the Bi- and Multi-Galileon, JHEP 07 (2013) 067 [arXiv:1303.0274] [INSPIRE].
S. Garcia-Saenz, Behavior of perturbations on spherically symmetric backgrounds in multi-Galileon theory, Phys. Rev. D 87 (2013) 104012 [arXiv:1303.2905] [INSPIRE].
L. Berezhiani, G. Chkareuli and G. Gabadadze, Restricted Galileons, Phys. Rev. D 88 (2013) 124020 [arXiv:1302.0549] [INSPIRE].
G. Gabadadze, R. Kimura and D. Pirtskhalava, Vainshtein Solutions Without Superluminal Modes, Phys. Rev. D 91 (2015) 124024 [arXiv:1412.8751] [INSPIRE].
K. Hinterbichler, A. Nicolis and M. Porrati, Superluminality in DGP, JHEP 09 (2009) 089 [arXiv:0905.2359] [INSPIRE].
S. Deser, A. Waldron and G. Zahariade, Propagation peculiarities of mean field massive gravity, Phys. Lett. B 749 (2015) 144 [arXiv:1504.02919] [INSPIRE].
P. Creminelli, M. Serone, G. Trevisan and E. Trincherini, Inequivalence of Coset Constructions for Spacetime Symmetries, JHEP 02 (2015) 037 [arXiv:1403.3095] [INSPIRE].
S.D. Mathur, The information paradox: A pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].
S.D. Mathur, The fuzzball proposal for black holes: An elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [INSPIRE].
G. Dvali and C. Gomez, Black Hole's Quantum N-Portrait, Fortsch. Phys. 61 (2013) 742 [arXiv:1112.3359] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].
G. Dvali, G.F. Giudice, C. Gomez and A. Kehagias, UV-Completion by Classicalization, JHEP 08 (2011) 108 [arXiv:1010.1415] [INSPIRE].
L. Keltner and A.J. Tolley, UV properties of Galileons: Spectral Densities, arXiv:1502.05706 [INSPIRE].
R. Klein, M. Ozkan and D. Roest, Galileons as the Scalar Analogue of General Relativity, Phys. Rev. D 93 (2016) 044053 [arXiv:1510.08864] [INSPIRE].
S.M. Carroll, Spacetime and geometry: An introduction to general relativity, Addison Wesley (2004).
C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, W.H. Freeman, San Francisco, U.S.A. (1973).
N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The string landscape, black holes and gravity as the weakest force, JHEP 06 (2007) 060 [hep-th/0601001] [INSPIRE].
X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality Constraints on Corrections to the Graviton Three-Point Coupling, JHEP 02 (2016) 020 [arXiv:1407.5597] [INSPIRE].
K. Benakli, S. Chapman, L. Darmé and Y. Oz, Superluminal graviton propagation, Phys. Rev. D 94 (2016) 084026 [arXiv:1512.07245] [INSPIRE].
J. Jing, S. Chen and Q. Pan, Geometric optics for a coupling model of electromagnetic and gravitational fields, Annals Phys. 367 (2016) 219 [arXiv:1510.03316] [INSPIRE].
R. Penrose, On Schwarzschild Causality — A Problem for “Lorentz Covariant” General Relativity, in Essays in General Relativity: A Festschrift for Abraham Taub, Academic Press (1980).
S. Gao and R.M. Wald, Theorems on gravitational time delay and related issues, Class. Quant. Grav. 17 (2000) 4999 [gr-qc/0007021] [INSPIRE].
S.D. Majumdar, A class of exact solutions of Einstein's field equations, Phys. Rev. 72 (1947) 390 [INSPIRE].
A. Papaetrou, A static solution of the equations of the gravitational field for an arbitrary charge distribution, Proc. Roy. Irish Acad. A 51 (1947) 191 [INSPIRE].
J.B. Hartle and S.W. Hawking, Solutions of the Einstein-Maxwell equations with many black holes, Commun. Math. Phys. 26 (1972) 87 [INSPIRE].
M.D. Schwartz, Quantum Field Theory and the Standard Model, Cambridge University Press, (2014).
E.T. Akhmedov, H. Godazgar and F.K. Popov, Hawking radiation and secularly growing loop corrections, Phys. Rev. D 93 (2016) 024029 [arXiv:1508.07500] [INSPIRE].
A. Kamenev, Field Theory of Non-Equilibrium Systems, Cambridge University Press, (2011).
S. Weinberg, Quantum contributions to cosmological correlations, Phys. Rev. D 72 (2005) 043514 [hep-th/0506236] [INSPIRE].
M.J. Duff, Quantum Tree Graphs and the Schwarzschild Solution, Phys. Rev. D 7 (1973) 2317 [INSPIRE].
M.J. Duff, Quantum corrections to the Schwarzschild solution, Phys. Rev. D 9 (1974) 1837 [INSPIRE].
G.W. Gibbons, Vacuum Polarization and the Spontaneous Loss of Charge by Black Holes, Commun. Math. Phys. 44 (1975) 245 [INSPIRE].
G. Goon and K. Hinterbichler, in preparation.
G. ’t Hooft and M.J.G. Veltman, One loop divergencies in the theory of gravitation, Annales Poincare Phys. Theor. A 20 (1974) 69.
M.H. Goro and A. Sagnotti, The Ultraviolet Behavior of Einstein Gravity, Nucl. Phys. B 266 (1986) 709 [INSPIRE].
D.M. Capper, M.J. Duff and L. Halpern, Photon corrections to the graviton propagator, Phys. Rev. D 10 (1974) 461 [INSPIRE].
J.F. Donoghue, B.R. Holstein, B. Garbrecht and T. Konstandin, Quantum corrections to the Reissner-Nordstrom and Kerr-Newman metrics, Phys. Lett. B 529 (2002) 132 [Erratum ibid. B 612 (2005) 311] [hep-th/0112237] [INSPIRE].
N.E.J. Bjerrum-Bohr, J.F. Donoghue and B.R. Holstein, Quantum corrections to the Schwarzschild and Kerr metrics, Phys. Rev. D 68 (2003) 084005 [Erratum ibid. D 71 (2005) 069904] [hep-th/0211071] [INSPIRE].
G.G. Kirilin, Quantum corrections to the Schwarzschild metric and reparametrization transformations, Phys. Rev. D 75 (2007) 108501 [gr-qc/0601020] [INSPIRE].
C.P. Burgess, Quantum gravity in everyday life: General relativity as an effective field theory, Living Rev. Rel. 7 (2004) 5 [gr-qc/0311082] [INSPIRE].
J.F. Donoghue, General relativity as an effective field theory: The leading quantum corrections, Phys. Rev. D 50 (1994) 3874 [gr-qc/9405057] [INSPIRE].
L.F. Abbott, Introduction to the Background Field Method, Acta Phys. Polon. B 13 (1982) 33 [INSPIRE].
D.A.R. Dalvit and F.D. Mazzitelli, Geodesics, gravitons and the gauge fixing problem, Phys. Rev. D 56 (1997) 7779 [hep-th/9708102] [INSPIRE].
A.O. Barvinsky and G.A. Vilkovisky, The Generalized Schwinger-Dewitt Technique in Gauge Theories and Quantum Gravity, Phys. Rept. 119 (1985) 1 [INSPIRE].
A. Andreassen, W. Frost and M.D. Schwartz, Consistent Use of Effective Potentials, Phys. Rev. D 91 (2015) 016009 [arXiv:1408.0287] [INSPIRE].
N.K. Nielsen, On the Gauge Dependence of Spontaneous Symmetry Breaking in Gauge Theories, Nucl. Phys. B 101 (1975) 173 [INSPIRE].
R. Fukuda and T. Kugo, Gauge Invariance in the Effective Action and Potential, Phys. Rev. D 13 (1976) 3469 [INSPIRE].
I.J.R. Aitchison and C.M. Fraser, Gauge Invariance and the Effective Potential, Annals Phys. 156 (1984) 1 [INSPIRE].
N.E.J. Bjerrum-Bohr, J.F. Donoghue and B.R. Holstein, Quantum gravitational corrections to the nonrelativistic scattering potential of two masses, Phys. Rev. D 67 (2003) 084033 [Erratum ibid. D 71 (2005) 069903] [hep-th/0211072] [INSPIRE].
I.B. Khriplovich and G.G. Kirilin, Quantum power correction to the Newton law, J. Exp. Theor. Phys. 95 (2002) 981 [gr-qc/0207118] [INSPIRE].
B.R. Holstein and A. Ross, Long Distance Effects in Mixed Electromagnetic-Gravitational Scattering, arXiv:0802.0717 [INSPIRE].
N.E.J. Bjerrum-Bohr, Leading quantum gravitational corrections to scalar QED, Phys. Rev. D 66 (2002) 084023 [hep-th/0206236] [INSPIRE].
S.L. Adler, Photon splitting and photon dispersion in a strong magnetic field, Annals Phys. 67 (1971) 599 [INSPIRE].
A.K. Harding and D. Lai, Physics of Strongly Magnetized Neutron Stars, Rept. Prog. Phys. 69 (2006) 2631 [astro-ph/0606674] [INSPIRE].
R. Ruffini, Y.-B. Wu and S.-S. Xue, Einstein-Euler-Heisenberg Theory and charged black holes, Phys. Rev. D 88 (2013) 085004 [arXiv:1307.4951] [INSPIRE].
H. Yajima and T. Tamaki, Black hole solutions in Euler-Heisenberg theory, Phys. Rev. D 63 (2001) 064007 [gr-qc/0005016] [INSPIRE].
Y. Kats, L. Motl and M. Padi, Higher-order corrections to mass-charge relation of extremal black holes, JHEP 12 (2007) 068 [hep-th/0606100] [INSPIRE].
D. Marolf and J. Polchinski, Gauge/Gravity Duality and the Black Hole Interior, Phys. Rev. Lett. 111 (2013) 171301 [arXiv:1307.4706] [INSPIRE].
W. Heisenberg and H. Euler, Consequences of Dirac’s theory of positrons, Z. Phys. 98 (1936) 714 [physics/0605038] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1609.00723
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Goon, G., Hinterbichler, K. Superluminality, black holes and EFT. J. High Energ. Phys. 2017, 134 (2017). https://doi.org/10.1007/JHEP02(2017)134
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2017)134