Abstract
Black holes (BHs) have many faces. Within the gauge/string duality they provide useful insights on strongly coupled quantum field theories and on quantum gravity. Furthermore, probing the strong curvature regime of any gravity theory, BHs carry the imprint of possible strong curvature corrections to General Relativity. Finally, beside their unique theoretical properties, compelling experimental evidence suggests that astrophysical BHs are very common objects in the universe. Here we discuss some applications of BH perturbation theory in various contexts. As applications in theoretical physics, we study perturbations of dilatonic BHs in Einstein-Maxwell theory and the holographic properties of the dual field theory via the Anti de Sitter/Condensed Matter duality. As applications in astrophysics, we discuss how the characteristic oscillations of BHs in string-inspired theories of gravity can provide observable signatures of deviations from Einstein’s theory. We study two well-motivated effective theories: Dynamical Chern-Simons gravity and Einstein-Dilatonic-Gauss-Bonnet gravity. We conclude by discussing the BH paradigm. Motivated by the lack of a definitive answer on the existence of astrophysical BHs, we study some viable alternatives, generically called “BH mimickers”. We focus on two representative cases: static thin-shell gravastars and superspinars, discussing their stability, gravitational-wave signature and viability as astrophysical objects.
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References
V. Cardoso, L. Gualtieri, C. Herdeiro, U. Sperhake, P.M. Chesler, NR/HEP: roadmap for the future, arXiv:1201.5118 [hep-th] (2012).
R. Narayan, New J. Phys. 7, 199 (2005) to appear in a forthcoming Special Focus Issue on Spacetime 100 Years Later published by the New Journal of Physics.
M. Cavaglia, Int. J. Mod. Phys. A 18, 1843 (2003).
J.M. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998).
G.T. Horowitz, J. Polchinski, Gauge/gravity duality, gr-qc/0602037 (2006).
S.A. Hartnoll, Class. Quantum Grav. 26, 224002 (2009).
T. Regge, J.A. Wheeler, Phys. Rev. 108, 1063 (1957).
F.J. Zerilli, Phys. Rev. D 2, 2141 (1970).
C.V. Vishveshwara, Phys. Rev. D 1, 2870 (1970).
H.-P. Nollert, Class. Quantum Grav. 16, R159 (1999).
K.D. Kokkotas, B.G. Schmidt, Living Rev. Relativ. 2, 2 (1999).
E. Berti, V. Cardoso, A.O. Starinets, Class. Quantum Grav. 26, 163001 (2009).
R. Konoplya, A. Zhidenko, Rev. Mod. Phys. 83, 793 (2011).
P. Pani, V. Cardoso, E. Berti, J. Read, M. Salgado, Phys. Rev. D 83, 081501 (2011).
F. Pretorius, Phys. Rev. Lett. 95, 121101 (2005).
M. Campanelli, C.O. Lousto, P. Marronetti, Y. Zlochower, Phys. Rev. Lett. 96, 111101 (2006).
F. Echeverria, Phys. Rev. D 40, 3194 (1989).
J.D. Bekenstein, Phys. Rev. Lett. 28, 452 (1972).
E. Berti, V. Cardoso, C.M. Will, Phys. Rev. D 73, 064030 (2006).
P.K. Kovtun, A.O. Starinets, Phys. Rev. D 72, 086009 (2005).
D.T. Son, A.O. Starinets, Ann. Rev. Nucl. Part. Sci. 57, 95 (2007).
S.K. Blau, Phys. Today 58, 23 (2005).
C.P. Herzog, J. Phys. A 42, 343001 (2009).
S.A. Hartnoll, C.P. Herzog, G.T. Horowitz, Phys. Rev. Lett. 101, 031601 (2008).
F. Benini, C.P. Herzog, R. Rahman, A. Yarom, JHEP 11, 2010 (137).
D.T. Son, Phys. Rev. D 78, 046003 (2008).
S.A. Hartnoll, J. Polchinski, E. Silverstein, D. Tong, JHEP 04, 2010 (120).
C.M. Will, Living Rev. Relativ. 9, 3 (2005).
A. Abramovici et al., Science 256, 325 (1992).
C.B.M.H. Chirenti, L. Rezzolla, Class. Quantum Grav. 24, 4191 (2007).
S. Alexander, N. Yunes, Phys. Rep. 480, 1 (2009).
B. Zwiebach, Phys. Lett. B 156, 315 (1985).
V. Cardoso, S. Chakrabarti, P. Pani, E. Berti, L. Gualtieri, Phys. Rev. Lett. 107, 241101 (2011).
N. Yunes, P. Pani, V. Cardoso Gravitational Waves from Extreme Mass-Ratio Inspirals as Probes of Scalar-Tensor Theories, arXiv:1112.3351v1 [gr-qc] (2011).
M. Visser, D.L. Wiltshire, Class. Quantum Grav. 21, 1135 (2004).
E.G. Gimon, P. Horava, Phys. Lett. B 672, 299 (2009).
P. Amaro-Seoane et al., Class. Quantum Grav. 24, R113 (2007).
D. Mateos, Class. Quantum Grav. 24, S713 (2007).
S. Sachdev, M. Mueller, J. Phys.: Condens. Matter 21, 2009 (164216).
J. McGreevy, Holographic duality with a view toward many-body physics, arXiv:0909.0518v3 [hep-th] (2009).
D.T. Son, A.O. Starinets, JHEP 09, 042 (2002).
G.W. Gibbons, K.-i. Maeda, Nucl. Phys. B 298, 741 (1988).
D. Garfinkle, G.T. Horowitz, A. Strominger, Phys. Rev. D 43, 3140 (1991).
S. Monni, M. Cadoni, Nucl. Phys. B 466, 101 (1996).
M.J. Duff, J.T. Liu, Nucl. Phys. B 554, 237 (1999).
S.S. Gubser, F.D. Rocha, Phys. Rev. D 81, 046001 (2010).
P. Breitenlohner, D.Z. Freedman, Phys. Lett. B 115, 197 (1982).
G. Dotti, R.J. Gleiser, Class. Quantum Grav. 22, L1 (2005).
M. Cadoni, G. D’Appollonio, P. Pani, JHEP 03, 100 (2010).
S.A. Hartnoll, C.P. Herzog, G.T. Horowitz, JHEP 12, 015 (2008).
K. Maeda, M. Natsuume, T. Okamura, Phys. Rev. D 79, 126004 (2009).
G.T. Horowitz, J.E. Santos, D. Tong, Optical Conductivity with Holographic Lattices, arXiv:1204.0519v1 [hep-th] (2012).
S.S. Gubser, F.D. Rocha, Phys. Rev. Lett. 102, 061601 (2009).
T. Albash, C.V. Johnson, JHEP 09, 121 (2008).
O. Domenech, M. Montull, A. Pomarol, A. Salvio, P.J. Silva, JHEP 08, 033 (2010).
M. Cadoni, P. Pani, JHEP 1104, 049 (2011).
P.P. Fiziev, D.R. Staicova, Two-dimensional generalization of the Muller root-finding algorithm and its applications, arXiv:1005.5375v2 [cs.NA] (2010).
G.T. Horowitz, Introduction to Holographic Superconductors, arXiv:1002.1722v2 [hep-th] (2010).
S.A. Hartnoll, P. Kovtun, Phys. Rev. D 76, 066001 (2007).
S.A. Hartnoll, C.P. Herzog, Phys. Rev. D 76, 106012 (2007).
K. Goldstein et al., JHEP 10, 2010 (027).
M. Cadoni, S. Mignemi, M. Serra, Phys. Rev. D 84, 084046 (2011).
M. Cadoni, P. Pani, M. Serra, JHEP 01, 091 (2010).
E. Berti, V. Cardoso, P. Pani, Phys. Rev. D 79, 101501 (2009).
G.T. Horowitz, V.E. Hubeny, Phys. Rev. D 62, 024027 (2000).
T. Harmark, J. Natario, R. Schiappa, Adv. Theor. Math. Phys. 14, 2010 (727).
S. Chandrasekhar, V. Ferrari, Proc. R. Soc. London A 434, 449 (1992).
S. Chandrasekhar, V. Ferrari, Proc. R. Soc. London A 437, 133 (1992).
J. Grain, A. Barrau, Nucl. Phys. B 742, 253 (2006).
G. Festuccia, H. Liu, A Bohr-Sommerfeld quantization formula for quasinormal frequencies of AdS black holes, arXiv:0811.1033v2 [gr-qc] (2008).
R.G. Daghigh, M.D. Green, Class. Quantum Grav. 26, 2009 (125017).
V. Cardoso, J.P.S. Lemos, Phys. Rev. D 64, 084017 (2001).
I.G. Moss, J.P. Norman, Class. Quantum Grav. 19, 2323 (2002).
G. Michalogiorgakis, S.S. Pufu, JHEP 02, 023 (2007).
I. Bakas, JHEP 01, 003 (2009).
J.V. Rocha, JHEP 08, 075 (2008).
R.A. Konoplya, Phys. Rev. D 66, 044009 (2002).
V. Cardoso, O.J.C. Dias, Phys. Rev. D 70, 084011 (2004).
E. Berti, K.D. Kokkotas, Phys. Rev. D 67, 064020 (2003).
V. Cardoso, O.J.C. Dias, S. Yoshida, Phys. Rev. D 74, 044008 (2006).
G. Gamow, Z. Phys. 51, 204 (1928).
S.A. Gurvitz, Phys. Rev. A 38, 1747 (1988).
B. Wang, C.-Y. Lin, C. Molina, Phys. Rev. D 70, 064025 (2004).
P. Pani, V. Cardoso, L. Gualtieri, E. Berti, A. Ishibashi, in preparation (2012).
C. Hoyle, D. Kapner, B. Heckel, E. Adelberger, J. Gundlach, U. Schmidt, H. Swanson, Phys. Rev. D 70, 042004 (2004).
S. Hawking, R. Penrose, The Nature of Space and Time: With a New Afterword by the Authors (Princeton University Press, Oxford, 2010).
A.G. Riess et al., Astron. J. 116, 1009 (1998).
S. Perlmutter et al., Astrophys. J. 517, 565 (1999).
D.N. Spergel et al., Astrophys. J. Suppl. 170, 377 (2007).
S.M. Carroll, Living Rev. Relativ. 4, 1 (2001).
P.J.E. Peebles, B. Ratra, Rev. Mod. Phys. 75, 559 (2003).
A. Dekel, F. Stoehr, G.A. Mamon, T.J. Cox, J.R. Primack, Nature 437, 707 (2005).
T. Clifton, P.G. Ferreira, A. Padilla, C. Skordis, Phys. Rep. 513, 1 (2012).
C. Brans, R.H. Dicke, Phys. Rev. 124, 925 (1961).
A.D.F. Shinji Tsujikawa, Living Rev. Relativ. 13, 3 (2010).
L. Blanchet, Living Rev. Relativ. 5, 3 (2002).
D. Psaltis, Living Rev. Relativ. 11, 9 (2008).
P. Pani, V. Cardoso, Phys. Rev. D 79, 084031 (2009).
C. Molina, P. Pani, V. Cardoso, L. Gualtieri, Phys. Rev. D 81, 124021 (2010).
P. Pani, V. Cardoso, T. Delsate, Phys. Rev. Lett. 107, 031101 (2011).
J. Casanellas, P. Pani, I. Lopes, V. Cardoso, Astrophys. J. 745, 15 (2012).
P. Pani, E. Berti, V. Cardoso, J. Read, Phys. Rev. D 84, 104035 (2011).
P. Pani, T. Delsate, V. Cardoso, Phys. Rev. D 85, 084020 (2012).
B. Caron et al., Class. Quantum Grav. 14, 1461 (1997).
E. Berti, A. Buonanno, C.M. Will, Phys. Rev. D 71, 084025 (2005).
C.M. Will, N. Yunes, Class. Quantum Grav. 21, 4367 (2004).
R. Ruffini, J. Wheeler, Phys. Today 24, 30 (1971).
B. Carter, Phys. Rev. Lett. 26, 331 (1971).
R.M. Wald, Phys. Rev. Lett. 26, 1653 (1971).
D.C. Robinson, Phys. Rev. Lett. 34, 905 (1975).
J.D. Bekenstein, Phys. Rev. D 5, 1239 (1972).
P. Bizon, Phys. Rev. Lett. 64, 2844 (1990).
S. Droz, M. Heusler, N. Straumann, Phys. Lett. B 268, 371 (1991).
S.S. Gubser, Class. Quantum Grav. 22, 5121 (2005).
S.S. Gubser, Phys. Rev. Lett. 101, 191601 (2008).
S.S. Gubser, Phys. Rev. D 78, 065034 (2008).
S.B. Giddings, S.D. Thomas, Phys. Rev. D 65, 056010 (2002).
P. Kanti, Int. J. Mod. Phys. A 19, 4899 (2004).
P. Kanti, Lect. Notes Phys. 769, 387 (2009).
G.W. Gibbons, Commun. Math. Phys. 44, 245 (1975).
J.D. Bekenstein, Phys. Rev. D 51, 6608 (1995).
J.R. Oppenheimer, H. Snyder, Phys. Rev. 56, 455 (1939).
R. Penrose, Phys. Rev. Lett. 14, 57 (1965).
R.H. Price, Phys. Rev. D 5, 2439 (1972).
R. Penrose, Riv. Nuovo Cimento 1, 252 (1969).
I. Hauser, F. Ernst, J. Math. Phys. 22, 1051 (1981).
F.D. Ryan, Phys. Rev. D 52, 5707 (1995).
P. Pani, C.F. Macedo, L.C. Crispino, V. Cardoso, Phys. Rev. D 84, 087501 (2011).
N. Yunes, L.C. Stein, Phys. Rev. D 83, 104002 (2011).
B.A. Campbell, N. Kaloper, K.A. Olive, Phys. Lett. B 285, 199 (1992).
S. Mignemi, N. Stewart, Phys. Lett. B 298, 299 (1993).
P. Kanti, N.E. Mavromatos, J. Rizos, K. Tamvakis, E. Winstanley, Phys. Rev. D 54, 5049 (1996).
T. Torii, H. Yajima, K.-i. Maeda, Phys. Rev. D 55, 739 (1997).
B. Kleihaus, J. Kunz, E. Radu, Phys. Rev. Lett. 106, 151104 (2011).
N. Yunes, F. Pretorius, Phys. Rev. D 79, 084043 (2009).
K. Konno, T. Matsuyama, S. Tanda, Prog. Theor. Phys. 122, 561 (2009).
N. Yunes, C.F. Sopuerta, Phys. Rev. D 77, 064007 (2008).
E. Barausse, T.P. Sotiriou, Phys. Rev. Lett. 101, 099001 (2008).
V. Cardoso, L. Gualtieri, Phys. Rev. D 80, 064008 (2009).
P. Pani, V. Cardoso, L. Gualtieri, Phys. Rev. D 83, 104048 (2011).
E. Berti, J. Cardoso, V. Cardoso, M. Cavaglia, Phys. Rev. D 76, 104044 (2007).
P. Amaro-Seoane, S. Aoudia, S. Babak, P. Binetruy, E. Berti, eLISA: Astrophysics and cosmology in the millihertz regime, arXiv:1201.3621 [astro-ph.CO] (2012).
Z.-K. Guo, N. Ohta, T. Torii, Prog. Theor. Phys. 120, 581 (2008).
K.-i. Maeda, N. Ohta, Y. Sasagawa, Phys. Rev. D 80, 104032 (2009).
S. Mignemi, N.R. Stewart, Phys. Rev. D 47, 5259 (1993).
P. Kanti, N.E. Mavromatos, J. Rizos, K. Tamvakis, E. Winstanley, Phys. Rev. D 57, 6255 (1998).
T. Kobayashi, H. Motohashi, T. Suyama, Black hole perturbation in the most general scalar-tensor theory with second-order field equations I: the odd-parity sector, arXiv:1202.4893 [gr-qc] (2012).
D. Psaltis, Probes and Tests of Strong-Field Gravity with Observations in the Electromagnetic Spectrum, arXiv:0806.1531 [astro-ph] (2008).
M. Visser, PoS BHS GR and strings, 001 (2008).
M.A. Abramowicz, W. Kluzniak, J.-P. Lasota, Astron. Astrophys. 396, L31 (2002).
F.E. Schunck, E.W. Mielke, Class. Quantum Grav. 20, R301 (2003).
D.F. Torres, S. Capozziello, G. Lambiase, Phys. Rev. D 62, 104012 (2000).
F.S. Guzman, Phys. Rev. D 73, 021501 (2006).
M. Kesden, J. Gair, M. Kamionkowski, Phys. Rev. D 71, 044015 (2005).
S. Yoshida, Y. Eriguchi, T. Futamase, Phys. Rev. D 50, 6235 (1994).
J. Balakrishna, R. Bondarescu, G. Daues, F. Siddhartha Guzman, E. Seidel, Class. Quantum Grav. 23, 2631 (2006).
E. Berti, V. Cardoso, Int. J. Mod. Phys. D 15, 2209 (2006).
P.O. Mazur, E. Mottola, Gravitational condensate stars, arXiv:gr-qc/0109035v5 (2001).
G. Chapline, E. Hohlfeld, R.B. Laughlin, D.I. Santiago, Int. J. Mod. Phys. A 18, 3587 (2003).
P.O. Mazur, E. Mottola, Proc. Natl. Acad. Sci. U.S.A. 101, 9545 (2004).
W. Israel, Nuovo Cimento B 44, Suppl. 10, 1 (1966).
J.L. Friedman, Commun. Math. Phys. 63, 243 (1978).
B.F. Schutz, N. Comins, Mon. Not. R. Astron. Soc. 182, 69 (1978).
Y. Zel’dovich, Zh. Eksp. Teor. Fiz. 14, 270 (1971) and Zh. Eksp. Teor. Fiz. 62.
C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (W.H. Freeman, San Francisco, 1973) ISBN 978-0-7167-0344-0.
V. Cardoso, P. Pani, M. Cadoni, M. Cavaglia, Phys. Rev. D 77, 124044 (2008).
V. Cardoso, P. Pani, M. Cadoni, M. Cavaglia, Class. Quantum Grav. 25, 195010 (2008).
P. Pani, V. Cardoso, M. Cadoni, M. Cavaglia, PoS BHS GR and strings, 027 (2008).
C.B.M.H. Chirenti, L. Rezzolla, Phys. Rev. D 78, 084011 (2008).
P.P. Fiziev, Class. Quantum Grav. 23, 2447 (2006).
P. Pani, E. Berti, V. Cardoso, Y. Chen, R. Norte, Phys. Rev. D 80, 124047 (2009).
M. Visser, Lorentzian Wormholes: From Einstein to Hawking (AIP, Woodbury, 1995) p. 412.
E. Poisson, M. Visser, Phys. Rev. D 52, 7318 (1995).
N. Andersson, Y. Kojima, K.D. Kokkotas, Astrophys. J. 462, 855 (1996).
K.D. Kokkotas, B.F. Schutz, Gen. Relativ. Gravit. 18, 913 (1986).
N. Andersson, Gen. Relativ. Gravit. 28, 1433 (1996).
M. Leins, H.P. Nollert, M.H. Soffel, Phys. Rev. D 48, 3467 (1993).
E. Berti, Gravitational waves from perturbed stars, PhD thesis.
S. Chandrasekhar, V. Ferrari, Proc. R. Soc. London A 432, 247 (1991).
Y. Kojima, Prog. Theor. Phys. 77, 297 (1987).
L. Gualtieri, E. Berti, J.A. Pons, G. Miniutti, V. Ferrari, Phys. Rev. D 64, 104007 (2001).
J.A. Pons, E. Berti, L. Gualtieri, G. Miniutti, V. Ferrari, Phys. Rev. D 65, 104021 (2002).
E. Berti, J.A. Pons, G. Miniutti, L. Gualtieri, V. Ferrari, Phys. Rev. D 66, 064013 (2002).
P. Pani, E. Barausse, E. Berti, V. Cardoso, Phys. Rev. D 82, 044009 (2010).
E. Poisson, Phys. Rev. D 47, 1497 (1993).
C. Cutler, E. Poisson, G.J. Sussman, L.S. Finn, Phys. Rev. D 47, 1511 (1993).
C. Cutler, D. Kennefick, E. Poisson, Phys. Rev. D 50, 3816 (1994).
E. Poisson, Phys. Rev. D 52, 5719 (1995).
E.E. Flanagan, T. Hinderer, Phys. Rev. D 77, 021502 (2008).
N. Yunes, E. Berti, Phys. Rev. D 77, 124006 (2008).
K.D. Kokkotas, J. Ruoff, N. Andersson, Phys. Rev. D 70, 043003 (2004).
T. Damour, S.N. Solodukhin, Phys. Rev. D 76, 024016 (2007).
G. Dotti, R. Gleiser, J. Pullin, Phys. Lett. B 644, 289 (2007).
G. Dotti, R.J. Gleiser, I.F. Ranea-Sandoval, H. Vucetich, Class. Quantum Grav. 25, 245012 (2008).
K. Hioki, K.-i. Maeda, Phys. Rev. D 80, 024042 (2009).
C. Bambi, N. Yoshida, Class. Quantum Grav. 27, 205006 (2010).
C. Reina, A. Treves, Astrophys. J. 227, 596 (1979).
C. Bambi, K. Freese, T. Harada, R. Takahashi, N. Yoshida, Phys. Rev. D 80, 104023 (2009).
C. Bambi, Numerical simulations of the accretion process in Kerr space-times with arbitrary value of the Kerr parameter, arXiv:0912.4944 [gr-qc] (2009).
R. Takahashi, T. Harada, Class. Quantum Grav. 27, 075003 (2010).
C. Bambi, T. Harada, R. Takahashi, N. Yoshida, Phys. Rev. D 81, 104004 (2010).
S. Chandrasekhar, Proc. R. Soc. London, Ser. A 392, 1 (1984).
S.A. Teukolsky, Phys. Rev. Lett. 29, 1114 (1972).
E. Berti, V. Cardoso, M. Casals, Phys. Rev. D 73, 024013 (2006).
S.A. Teukolsky, W.H. Press, Astrophys. J. 193, 443 (1974).
E.W. Leaver, Proc. R. Soc. London A 402, 285 (1985).
W.H. Press, S.A. Teukolsky, Nature 238, 211 (1972).
J.M. Bardeen, Nature 226, 64 (1970).
R. Wald, Ann. Phys. 82, 548 (1974).
A.R. King, J.E. Pringle, J.A. Hofmann, Mon. Not. R. Astron. Soc. 385, 1621 (2008).
L.W. Brenneman, C.S. Reynolds, Astrophys. J. 652, 1028 (2006).
U. Sperhake et al., Phys. Rev. Lett. 103, 131102 (2009).
E. Berti, M. Volonteri, Astrophys. J. 684, 822 (2008).
L. Rezzolla, E.N. Dorband, C. Reisswig, P. Diener, D. Pollney, E. Schnetter, B. Szilágyi, Astrophys. J. 679, 1422 (2008).
L. Rezzolla, E. Barausse, E.N. Dorband, D. Pollney, C. Reisswig, J. Seiler, S. Husa, Phys. Rev. D 78, 044002 (2008).
E. Barausse, L. Rezzolla, Astrophys. J. Lett. 704, L40 (2009).
M. Kesden, G. Lockhart, E.S. Phinney, Phys. Rev. D 82, 124045 (2010).
M. Volonteri, P. Madau, E. Quataert, M.J. Rees, Astrophys. J. 620, 69 (2005).
A.R. King, U. Kolb, Mon. Not. R. Astron. Soc. 305, 654 (1999).
K. Belczynski, R.E. Taam, E. Rantsiou, M. van der Sluys, Astrophys. J. 682, 474 (2008).
G.B. Cook, S.L. Shapiro, S.A. Teukolsky, Astrophys. J. 424, 823 (1994).
E. Berti, N. Stergioulas, Mon. Not. R. Astron. Soc. 350, 1416 (2004).
B. Giacomazzo, L. Rezzolla, N. Stergioulas, Phys. Rev. D 84, 024022 (2011).
L. Baiotti, I. Hawke, P.J. Montero, F. Löffler, L. Rezzolla, N. Stergioulas, J.A. Font, E. Seidel, Phys. Rev. D 71, 024035 (2005).
S.R. Dolan, Phys. Rev. D 82, 104003 (2010).
B. Carter, Phys. Rev. 174, 1559 (1968).
D. Psaltis, D. Perrodin, K.R. Dienes, I. Mocioiu, Phys. Rev. Lett. 100, 091101 (2008).
E. Barausse, T.P. Sotiriou, Phys. Rev. Lett. 101, 099001 (2008).
T.P. Sotiriou, V. Faraoni, Rev. Mod. Phys. 82, 451 (2010).
D. Wands, Class. Quantum Grav. 11, 269 (1994).
C.M. Will, H.W. Zaglauer, Astrophys. J. 346, 366 (1989).
L. Brenneman, C. Reynolds, M. Nowak, R. Reis, M. Trippe et al., Astrophys. J. 736, 103 (2011).
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This paper is based on the author’s PhD thesis, that was awarded the INFN “Sergio Fubini” Prize in 2011.
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Pani, P. Applications of black hole perturbation theory. Eur. Phys. J. Plus 127, 67 (2012). https://doi.org/10.1140/epjp/i2012-12067-1
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DOI: https://doi.org/10.1140/epjp/i2012-12067-1
Keywords
- Event Horizon
- Unstable Mode
- Gravitational Perturbation
- Scalar Condensate
- Boson Star