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Applications of black hole perturbation theory

From the gauge/string duality to high-energy astrophysics

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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

  1. V. Cardoso, L. Gualtieri, C. Herdeiro, U. Sperhake, P.M. Chesler, NR/HEP: roadmap for the future, arXiv:1201.5118 [hep-th] (2012).

  2. 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.

    MathSciNet  ADS  Google Scholar 

  3. M. Cavaglia, Int. J. Mod. Phys. A 18, 1843 (2003).

    MathSciNet  ADS  MATH  Google Scholar 

  4. J.M. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998).

    MathSciNet  ADS  MATH  Google Scholar 

  5. G.T. Horowitz, J. Polchinski, Gauge/gravity duality, gr-qc/0602037 (2006).

  6. S.A. Hartnoll, Class. Quantum Grav. 26, 224002 (2009).

    MathSciNet  ADS  Google Scholar 

  7. T. Regge, J.A. Wheeler, Phys. Rev. 108, 1063 (1957).

    MathSciNet  ADS  MATH  Google Scholar 

  8. F.J. Zerilli, Phys. Rev. D 2, 2141 (1970).

    MathSciNet  ADS  MATH  Google Scholar 

  9. C.V. Vishveshwara, Phys. Rev. D 1, 2870 (1970).

    ADS  Google Scholar 

  10. H.-P. Nollert, Class. Quantum Grav. 16, R159 (1999).

    MathSciNet  ADS  MATH  Google Scholar 

  11. K.D. Kokkotas, B.G. Schmidt, Living Rev. Relativ. 2, 2 (1999).

    MathSciNet  ADS  Google Scholar 

  12. E. Berti, V. Cardoso, A.O. Starinets, Class. Quantum Grav. 26, 163001 (2009).

    MathSciNet  ADS  Google Scholar 

  13. R. Konoplya, A. Zhidenko, Rev. Mod. Phys. 83, 793 (2011).

    ADS  Google Scholar 

  14. P. Pani, V. Cardoso, E. Berti, J. Read, M. Salgado, Phys. Rev. D 83, 081501 (2011).

    ADS  Google Scholar 

  15. F. Pretorius, Phys. Rev. Lett. 95, 121101 (2005).

    MathSciNet  ADS  Google Scholar 

  16. M. Campanelli, C.O. Lousto, P. Marronetti, Y. Zlochower, Phys. Rev. Lett. 96, 111101 (2006).

    ADS  Google Scholar 

  17. F. Echeverria, Phys. Rev. D 40, 3194 (1989).

    ADS  Google Scholar 

  18. J.D. Bekenstein, Phys. Rev. Lett. 28, 452 (1972).

    ADS  Google Scholar 

  19. E. Berti, V. Cardoso, C.M. Will, Phys. Rev. D 73, 064030 (2006).

    MathSciNet  ADS  Google Scholar 

  20. P.K. Kovtun, A.O. Starinets, Phys. Rev. D 72, 086009 (2005).

    ADS  Google Scholar 

  21. D.T. Son, A.O. Starinets, Ann. Rev. Nucl. Part. Sci. 57, 95 (2007).

    ADS  Google Scholar 

  22. S.K. Blau, Phys. Today 58, 23 (2005).

    ADS  Google Scholar 

  23. C.P. Herzog, J. Phys. A 42, 343001 (2009).

    MathSciNet  Google Scholar 

  24. S.A. Hartnoll, C.P. Herzog, G.T. Horowitz, Phys. Rev. Lett. 101, 031601 (2008).

    ADS  Google Scholar 

  25. F. Benini, C.P. Herzog, R. Rahman, A. Yarom, JHEP 11, 2010 (137).

  26. D.T. Son, Phys. Rev. D 78, 046003 (2008).

    MathSciNet  ADS  Google Scholar 

  27. S.A. Hartnoll, J. Polchinski, E. Silverstein, D. Tong, JHEP 04, 2010 (120).

  28. C.M. Will, Living Rev. Relativ. 9, 3 (2005).

    ADS  Google Scholar 

  29. A. Abramovici et al., Science 256, 325 (1992).

    ADS  Google Scholar 

  30. C.B.M.H. Chirenti, L. Rezzolla, Class. Quantum Grav. 24, 4191 (2007).

    MathSciNet  ADS  MATH  Google Scholar 

  31. S. Alexander, N. Yunes, Phys. Rep. 480, 1 (2009).

    MathSciNet  ADS  Google Scholar 

  32. B. Zwiebach, Phys. Lett. B 156, 315 (1985).

    ADS  Google Scholar 

  33. V. Cardoso, S. Chakrabarti, P. Pani, E. Berti, L. Gualtieri, Phys. Rev. Lett. 107, 241101 (2011).

    ADS  Google Scholar 

  34. 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).

    ADS  Google Scholar 

  35. M. Visser, D.L. Wiltshire, Class. Quantum Grav. 21, 1135 (2004).

    MathSciNet  ADS  MATH  Google Scholar 

  36. E.G. Gimon, P. Horava, Phys. Lett. B 672, 299 (2009).

    MathSciNet  ADS  Google Scholar 

  37. P. Amaro-Seoane et al., Class. Quantum Grav. 24, R113 (2007).

    MathSciNet  ADS  MATH  Google Scholar 

  38. D. Mateos, Class. Quantum Grav. 24, S713 (2007).

    MathSciNet  ADS  MATH  Google Scholar 

  39. S. Sachdev, M. Mueller, J. Phys.: Condens. Matter 21, 2009 (164216).

  40. J. McGreevy, Holographic duality with a view toward many-body physics, arXiv:0909.0518v3 [hep-th] (2009).

  41. D.T. Son, A.O. Starinets, JHEP 09, 042 (2002).

    MathSciNet  ADS  Google Scholar 

  42. G.W. Gibbons, K.-i. Maeda, Nucl. Phys. B 298, 741 (1988).

    MathSciNet  ADS  Google Scholar 

  43. D. Garfinkle, G.T. Horowitz, A. Strominger, Phys. Rev. D 43, 3140 (1991).

    MathSciNet  ADS  Google Scholar 

  44. S. Monni, M. Cadoni, Nucl. Phys. B 466, 101 (1996).

    MathSciNet  ADS  MATH  Google Scholar 

  45. M.J. Duff, J.T. Liu, Nucl. Phys. B 554, 237 (1999).

    MathSciNet  ADS  MATH  Google Scholar 

  46. S.S. Gubser, F.D. Rocha, Phys. Rev. D 81, 046001 (2010).

    MathSciNet  ADS  Google Scholar 

  47. P. Breitenlohner, D.Z. Freedman, Phys. Lett. B 115, 197 (1982).

    MathSciNet  ADS  Google Scholar 

  48. G. Dotti, R.J. Gleiser, Class. Quantum Grav. 22, L1 (2005).

    MathSciNet  ADS  MATH  Google Scholar 

  49. M. Cadoni, G. D’Appollonio, P. Pani, JHEP 03, 100 (2010).

    MathSciNet  ADS  Google Scholar 

  50. S.A. Hartnoll, C.P. Herzog, G.T. Horowitz, JHEP 12, 015 (2008).

    MathSciNet  ADS  Google Scholar 

  51. K. Maeda, M. Natsuume, T. Okamura, Phys. Rev. D 79, 126004 (2009).

    ADS  Google Scholar 

  52. G.T. Horowitz, J.E. Santos, D. Tong, Optical Conductivity with Holographic Lattices, arXiv:1204.0519v1 [hep-th] (2012).

  53. S.S. Gubser, F.D. Rocha, Phys. Rev. Lett. 102, 061601 (2009).

    MathSciNet  ADS  Google Scholar 

  54. T. Albash, C.V. Johnson, JHEP 09, 121 (2008).

    MathSciNet  ADS  Google Scholar 

  55. O. Domenech, M. Montull, A. Pomarol, A. Salvio, P.J. Silva, JHEP 08, 033 (2010).

    ADS  Google Scholar 

  56. M. Cadoni, P. Pani, JHEP 1104, 049 (2011).

    ADS  Google Scholar 

  57. P.P. Fiziev, D.R. Staicova, Two-dimensional generalization of the Muller root-finding algorithm and its applications, arXiv:1005.5375v2 [cs.NA] (2010).

  58. G.T. Horowitz, Introduction to Holographic Superconductors, arXiv:1002.1722v2 [hep-th] (2010).

  59. S.A. Hartnoll, P. Kovtun, Phys. Rev. D 76, 066001 (2007).

    ADS  Google Scholar 

  60. S.A. Hartnoll, C.P. Herzog, Phys. Rev. D 76, 106012 (2007).

    MathSciNet  ADS  Google Scholar 

  61. K. Goldstein et al., JHEP 10, 2010 (027).

  62. M. Cadoni, S. Mignemi, M. Serra, Phys. Rev. D 84, 084046 (2011).

    ADS  Google Scholar 

  63. M. Cadoni, P. Pani, M. Serra, JHEP 01, 091 (2010).

    MathSciNet  ADS  Google Scholar 

  64. E. Berti, V. Cardoso, P. Pani, Phys. Rev. D 79, 101501 (2009).

    MathSciNet  ADS  Google Scholar 

  65. G.T. Horowitz, V.E. Hubeny, Phys. Rev. D 62, 024027 (2000).

    MathSciNet  ADS  Google Scholar 

  66. T. Harmark, J. Natario, R. Schiappa, Adv. Theor. Math. Phys. 14, 2010 (727).

  67. S. Chandrasekhar, V. Ferrari, Proc. R. Soc. London A 434, 449 (1992).

    MathSciNet  ADS  Google Scholar 

  68. S. Chandrasekhar, V. Ferrari, Proc. R. Soc. London A 437, 133 (1992).

    MathSciNet  ADS  Google Scholar 

  69. J. Grain, A. Barrau, Nucl. Phys. B 742, 253 (2006).

    ADS  MATH  Google Scholar 

  70. G. Festuccia, H. Liu, A Bohr-Sommerfeld quantization formula for quasinormal frequencies of AdS black holes, arXiv:0811.1033v2 [gr-qc] (2008).

  71. R.G. Daghigh, M.D. Green, Class. Quantum Grav. 26, 2009 (125017).

  72. V. Cardoso, J.P.S. Lemos, Phys. Rev. D 64, 084017 (2001).

    MathSciNet  ADS  Google Scholar 

  73. I.G. Moss, J.P. Norman, Class. Quantum Grav. 19, 2323 (2002).

    MathSciNet  ADS  MATH  Google Scholar 

  74. G. Michalogiorgakis, S.S. Pufu, JHEP 02, 023 (2007).

    MathSciNet  ADS  Google Scholar 

  75. I. Bakas, JHEP 01, 003 (2009).

    MathSciNet  ADS  Google Scholar 

  76. J.V. Rocha, JHEP 08, 075 (2008).

    MathSciNet  ADS  Google Scholar 

  77. R.A. Konoplya, Phys. Rev. D 66, 044009 (2002).

    MathSciNet  ADS  Google Scholar 

  78. V. Cardoso, O.J.C. Dias, Phys. Rev. D 70, 084011 (2004).

    MathSciNet  ADS  Google Scholar 

  79. E. Berti, K.D. Kokkotas, Phys. Rev. D 67, 064020 (2003).

    MathSciNet  ADS  Google Scholar 

  80. V. Cardoso, O.J.C. Dias, S. Yoshida, Phys. Rev. D 74, 044008 (2006).

    ADS  Google Scholar 

  81. G. Gamow, Z. Phys. 51, 204 (1928).

    ADS  MATH  Google Scholar 

  82. S.A. Gurvitz, Phys. Rev. A 38, 1747 (1988).

    ADS  Google Scholar 

  83. B. Wang, C.-Y. Lin, C. Molina, Phys. Rev. D 70, 064025 (2004).

    MathSciNet  ADS  Google Scholar 

  84. P. Pani, V. Cardoso, L. Gualtieri, E. Berti, A. Ishibashi, in preparation (2012).

  85. C. Hoyle, D. Kapner, B. Heckel, E. Adelberger, J. Gundlach, U. Schmidt, H. Swanson, Phys. Rev. D 70, 042004 (2004).

    ADS  Google Scholar 

  86. S. Hawking, R. Penrose, The Nature of Space and Time: With a New Afterword by the Authors (Princeton University Press, Oxford, 2010).

  87. A.G. Riess et al., Astron. J. 116, 1009 (1998).

    ADS  Google Scholar 

  88. S. Perlmutter et al., Astrophys. J. 517, 565 (1999).

    ADS  Google Scholar 

  89. D.N. Spergel et al., Astrophys. J. Suppl. 170, 377 (2007).

    ADS  Google Scholar 

  90. S.M. Carroll, Living Rev. Relativ. 4, 1 (2001).

    ADS  Google Scholar 

  91. P.J.E. Peebles, B. Ratra, Rev. Mod. Phys. 75, 559 (2003).

    MathSciNet  ADS  MATH  Google Scholar 

  92. A. Dekel, F. Stoehr, G.A. Mamon, T.J. Cox, J.R. Primack, Nature 437, 707 (2005).

    ADS  Google Scholar 

  93. T. Clifton, P.G. Ferreira, A. Padilla, C. Skordis, Phys. Rep. 513, 1 (2012).

    MathSciNet  ADS  Google Scholar 

  94. C. Brans, R.H. Dicke, Phys. Rev. 124, 925 (1961).

    MathSciNet  ADS  MATH  Google Scholar 

  95. A.D.F. Shinji Tsujikawa, Living Rev. Relativ. 13, 3 (2010).

    ADS  Google Scholar 

  96. L. Blanchet, Living Rev. Relativ. 5, 3 (2002).

    ADS  Google Scholar 

  97. D. Psaltis, Living Rev. Relativ. 11, 9 (2008).

    ADS  Google Scholar 

  98. P. Pani, V. Cardoso, Phys. Rev. D 79, 084031 (2009).

    MathSciNet  ADS  Google Scholar 

  99. C. Molina, P. Pani, V. Cardoso, L. Gualtieri, Phys. Rev. D 81, 124021 (2010).

    ADS  Google Scholar 

  100. P. Pani, V. Cardoso, T. Delsate, Phys. Rev. Lett. 107, 031101 (2011).

    ADS  Google Scholar 

  101. J. Casanellas, P. Pani, I. Lopes, V. Cardoso, Astrophys. J. 745, 15 (2012).

    ADS  Google Scholar 

  102. P. Pani, E. Berti, V. Cardoso, J. Read, Phys. Rev. D 84, 104035 (2011).

    ADS  Google Scholar 

  103. P. Pani, T. Delsate, V. Cardoso, Phys. Rev. D 85, 084020 (2012).

    ADS  Google Scholar 

  104. B. Caron et al., Class. Quantum Grav. 14, 1461 (1997).

    ADS  Google Scholar 

  105. E. Berti, A. Buonanno, C.M. Will, Phys. Rev. D 71, 084025 (2005).

    ADS  Google Scholar 

  106. C.M. Will, N. Yunes, Class. Quantum Grav. 21, 4367 (2004).

    ADS  MATH  Google Scholar 

  107. R. Ruffini, J. Wheeler, Phys. Today 24, 30 (1971).

    ADS  Google Scholar 

  108. B. Carter, Phys. Rev. Lett. 26, 331 (1971).

    ADS  Google Scholar 

  109. R.M. Wald, Phys. Rev. Lett. 26, 1653 (1971).

    ADS  Google Scholar 

  110. D.C. Robinson, Phys. Rev. Lett. 34, 905 (1975).

    ADS  Google Scholar 

  111. J.D. Bekenstein, Phys. Rev. D 5, 1239 (1972).

    MathSciNet  ADS  Google Scholar 

  112. P. Bizon, Phys. Rev. Lett. 64, 2844 (1990).

    MathSciNet  ADS  MATH  Google Scholar 

  113. S. Droz, M. Heusler, N. Straumann, Phys. Lett. B 268, 371 (1991).

    MathSciNet  ADS  Google Scholar 

  114. S.S. Gubser, Class. Quantum Grav. 22, 5121 (2005).

    MathSciNet  ADS  MATH  Google Scholar 

  115. S.S. Gubser, Phys. Rev. Lett. 101, 191601 (2008).

    MathSciNet  ADS  Google Scholar 

  116. S.S. Gubser, Phys. Rev. D 78, 065034 (2008).

    ADS  Google Scholar 

  117. S.B. Giddings, S.D. Thomas, Phys. Rev. D 65, 056010 (2002).

    ADS  Google Scholar 

  118. P. Kanti, Int. J. Mod. Phys. A 19, 4899 (2004).

    MathSciNet  ADS  MATH  Google Scholar 

  119. P. Kanti, Lect. Notes Phys. 769, 387 (2009).

    MathSciNet  ADS  Google Scholar 

  120. G.W. Gibbons, Commun. Math. Phys. 44, 245 (1975).

    MathSciNet  ADS  Google Scholar 

  121. J.D. Bekenstein, Phys. Rev. D 51, 6608 (1995).

    MathSciNet  ADS  Google Scholar 

  122. J.R. Oppenheimer, H. Snyder, Phys. Rev. 56, 455 (1939).

    ADS  MATH  Google Scholar 

  123. R. Penrose, Phys. Rev. Lett. 14, 57 (1965).

    MathSciNet  ADS  MATH  Google Scholar 

  124. R.H. Price, Phys. Rev. D 5, 2439 (1972).

    MathSciNet  ADS  Google Scholar 

  125. R. Penrose, Riv. Nuovo Cimento 1, 252 (1969).

    Google Scholar 

  126. I. Hauser, F. Ernst, J. Math. Phys. 22, 1051 (1981).

    MathSciNet  ADS  MATH  Google Scholar 

  127. F.D. Ryan, Phys. Rev. D 52, 5707 (1995).

    ADS  Google Scholar 

  128. P. Pani, C.F. Macedo, L.C. Crispino, V. Cardoso, Phys. Rev. D 84, 087501 (2011).

    ADS  Google Scholar 

  129. N. Yunes, L.C. Stein, Phys. Rev. D 83, 104002 (2011).

    ADS  Google Scholar 

  130. B.A. Campbell, N. Kaloper, K.A. Olive, Phys. Lett. B 285, 199 (1992).

    MathSciNet  ADS  Google Scholar 

  131. S. Mignemi, N. Stewart, Phys. Lett. B 298, 299 (1993).

    ADS  Google Scholar 

  132. P. Kanti, N.E. Mavromatos, J. Rizos, K. Tamvakis, E. Winstanley, Phys. Rev. D 54, 5049 (1996).

    MathSciNet  ADS  Google Scholar 

  133. T. Torii, H. Yajima, K.-i. Maeda, Phys. Rev. D 55, 739 (1997).

    MathSciNet  ADS  Google Scholar 

  134. B. Kleihaus, J. Kunz, E. Radu, Phys. Rev. Lett. 106, 151104 (2011).

    ADS  Google Scholar 

  135. N. Yunes, F. Pretorius, Phys. Rev. D 79, 084043 (2009).

    ADS  Google Scholar 

  136. K. Konno, T. Matsuyama, S. Tanda, Prog. Theor. Phys. 122, 561 (2009).

    ADS  MATH  Google Scholar 

  137. N. Yunes, C.F. Sopuerta, Phys. Rev. D 77, 064007 (2008).

    MathSciNet  ADS  Google Scholar 

  138. E. Barausse, T.P. Sotiriou, Phys. Rev. Lett. 101, 099001 (2008).

    ADS  Google Scholar 

  139. V. Cardoso, L. Gualtieri, Phys. Rev. D 80, 064008 (2009).

    ADS  Google Scholar 

  140. P. Pani, V. Cardoso, L. Gualtieri, Phys. Rev. D 83, 104048 (2011).

    ADS  Google Scholar 

  141. E. Berti, J. Cardoso, V. Cardoso, M. Cavaglia, Phys. Rev. D 76, 104044 (2007).

    ADS  Google Scholar 

  142. 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).

  143. Z.-K. Guo, N. Ohta, T. Torii, Prog. Theor. Phys. 120, 581 (2008).

    ADS  MATH  Google Scholar 

  144. K.-i. Maeda, N. Ohta, Y. Sasagawa, Phys. Rev. D 80, 104032 (2009).

    MathSciNet  ADS  Google Scholar 

  145. S. Mignemi, N.R. Stewart, Phys. Rev. D 47, 5259 (1993).

    MathSciNet  ADS  Google Scholar 

  146. P. Kanti, N.E. Mavromatos, J. Rizos, K. Tamvakis, E. Winstanley, Phys. Rev. D 57, 6255 (1998).

    MathSciNet  ADS  Google Scholar 

  147. 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).

  148. D. Psaltis, Probes and Tests of Strong-Field Gravity with Observations in the Electromagnetic Spectrum, arXiv:0806.1531 [astro-ph] (2008).

  149. M. Visser, PoS BHS GR and strings, 001 (2008).

    Google Scholar 

  150. M.A. Abramowicz, W. Kluzniak, J.-P. Lasota, Astron. Astrophys. 396, L31 (2002).

    ADS  MATH  Google Scholar 

  151. F.E. Schunck, E.W. Mielke, Class. Quantum Grav. 20, R301 (2003).

    MathSciNet  ADS  MATH  Google Scholar 

  152. D.F. Torres, S. Capozziello, G. Lambiase, Phys. Rev. D 62, 104012 (2000).

    ADS  Google Scholar 

  153. F.S. Guzman, Phys. Rev. D 73, 021501 (2006).

    ADS  Google Scholar 

  154. M. Kesden, J. Gair, M. Kamionkowski, Phys. Rev. D 71, 044015 (2005).

    ADS  Google Scholar 

  155. S. Yoshida, Y. Eriguchi, T. Futamase, Phys. Rev. D 50, 6235 (1994).

    ADS  Google Scholar 

  156. J. Balakrishna, R. Bondarescu, G. Daues, F. Siddhartha Guzman, E. Seidel, Class. Quantum Grav. 23, 2631 (2006).

    MathSciNet  ADS  MATH  Google Scholar 

  157. E. Berti, V. Cardoso, Int. J. Mod. Phys. D 15, 2209 (2006).

    MathSciNet  ADS  MATH  Google Scholar 

  158. P.O. Mazur, E. Mottola, Gravitational condensate stars, arXiv:gr-qc/0109035v5 (2001).

  159. G. Chapline, E. Hohlfeld, R.B. Laughlin, D.I. Santiago, Int. J. Mod. Phys. A 18, 3587 (2003).

    ADS  Google Scholar 

  160. P.O. Mazur, E. Mottola, Proc. Natl. Acad. Sci. U.S.A. 101, 9545 (2004).

    ADS  Google Scholar 

  161. W. Israel, Nuovo Cimento B 44, Suppl. 10, 1 (1966).

    Google Scholar 

  162. J.L. Friedman, Commun. Math. Phys. 63, 243 (1978).

    ADS  MATH  Google Scholar 

  163. B.F. Schutz, N. Comins, Mon. Not. R. Astron. Soc. 182, 69 (1978).

    ADS  Google Scholar 

  164. Y. Zel’dovich, Zh. Eksp. Teor. Fiz. 14, 270 (1971) and Zh. Eksp. Teor. Fiz. 62.

    Google Scholar 

  165. C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (W.H. Freeman, San Francisco, 1973) ISBN 978-0-7167-0344-0.

  166. V. Cardoso, P. Pani, M. Cadoni, M. Cavaglia, Phys. Rev. D 77, 124044 (2008).

    ADS  Google Scholar 

  167. V. Cardoso, P. Pani, M. Cadoni, M. Cavaglia, Class. Quantum Grav. 25, 195010 (2008).

    MathSciNet  ADS  Google Scholar 

  168. P. Pani, V. Cardoso, M. Cadoni, M. Cavaglia, PoS BHS GR and strings, 027 (2008).

    Google Scholar 

  169. C.B.M.H. Chirenti, L. Rezzolla, Phys. Rev. D 78, 084011 (2008).

    ADS  Google Scholar 

  170. P.P. Fiziev, Class. Quantum Grav. 23, 2447 (2006).

    MathSciNet  ADS  MATH  Google Scholar 

  171. P. Pani, E. Berti, V. Cardoso, Y. Chen, R. Norte, Phys. Rev. D 80, 124047 (2009).

    ADS  Google Scholar 

  172. M. Visser, Lorentzian Wormholes: From Einstein to Hawking (AIP, Woodbury, 1995) p. 412.

  173. E. Poisson, M. Visser, Phys. Rev. D 52, 7318 (1995).

    MathSciNet  ADS  Google Scholar 

  174. N. Andersson, Y. Kojima, K.D. Kokkotas, Astrophys. J. 462, 855 (1996).

    ADS  Google Scholar 

  175. K.D. Kokkotas, B.F. Schutz, Gen. Relativ. Gravit. 18, 913 (1986).

    ADS  MATH  Google Scholar 

  176. N. Andersson, Gen. Relativ. Gravit. 28, 1433 (1996).

    ADS  MATH  Google Scholar 

  177. M. Leins, H.P. Nollert, M.H. Soffel, Phys. Rev. D 48, 3467 (1993).

    ADS  Google Scholar 

  178. E. Berti, Gravitational waves from perturbed stars, PhD thesis.

  179. S. Chandrasekhar, V. Ferrari, Proc. R. Soc. London A 432, 247 (1991).

    MathSciNet  ADS  Google Scholar 

  180. Y. Kojima, Prog. Theor. Phys. 77, 297 (1987).

    ADS  Google Scholar 

  181. L. Gualtieri, E. Berti, J.A. Pons, G. Miniutti, V. Ferrari, Phys. Rev. D 64, 104007 (2001).

    ADS  Google Scholar 

  182. J.A. Pons, E. Berti, L. Gualtieri, G. Miniutti, V. Ferrari, Phys. Rev. D 65, 104021 (2002).

    ADS  Google Scholar 

  183. E. Berti, J.A. Pons, G. Miniutti, L. Gualtieri, V. Ferrari, Phys. Rev. D 66, 064013 (2002).

    ADS  Google Scholar 

  184. P. Pani, E. Barausse, E. Berti, V. Cardoso, Phys. Rev. D 82, 044009 (2010).

    ADS  Google Scholar 

  185. E. Poisson, Phys. Rev. D 47, 1497 (1993).

    MathSciNet  ADS  Google Scholar 

  186. C. Cutler, E. Poisson, G.J. Sussman, L.S. Finn, Phys. Rev. D 47, 1511 (1993).

    MathSciNet  ADS  Google Scholar 

  187. C. Cutler, D. Kennefick, E. Poisson, Phys. Rev. D 50, 3816 (1994).

    ADS  Google Scholar 

  188. E. Poisson, Phys. Rev. D 52, 5719 (1995).

    MathSciNet  ADS  Google Scholar 

  189. E.E. Flanagan, T. Hinderer, Phys. Rev. D 77, 021502 (2008).

    ADS  Google Scholar 

  190. N. Yunes, E. Berti, Phys. Rev. D 77, 124006 (2008).

    ADS  Google Scholar 

  191. K.D. Kokkotas, J. Ruoff, N. Andersson, Phys. Rev. D 70, 043003 (2004).

    ADS  Google Scholar 

  192. T. Damour, S.N. Solodukhin, Phys. Rev. D 76, 024016 (2007).

    MathSciNet  ADS  Google Scholar 

  193. G. Dotti, R. Gleiser, J. Pullin, Phys. Lett. B 644, 289 (2007).

    ADS  MATH  Google Scholar 

  194. G. Dotti, R.J. Gleiser, I.F. Ranea-Sandoval, H. Vucetich, Class. Quantum Grav. 25, 245012 (2008).

    MathSciNet  ADS  Google Scholar 

  195. K. Hioki, K.-i. Maeda, Phys. Rev. D 80, 024042 (2009).

    ADS  Google Scholar 

  196. C. Bambi, N. Yoshida, Class. Quantum Grav. 27, 205006 (2010).

    MathSciNet  ADS  Google Scholar 

  197. C. Reina, A. Treves, Astrophys. J. 227, 596 (1979).

    ADS  Google Scholar 

  198. C. Bambi, K. Freese, T. Harada, R. Takahashi, N. Yoshida, Phys. Rev. D 80, 104023 (2009).

    ADS  Google Scholar 

  199. 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).

  200. R. Takahashi, T. Harada, Class. Quantum Grav. 27, 075003 (2010).

    MathSciNet  ADS  Google Scholar 

  201. C. Bambi, T. Harada, R. Takahashi, N. Yoshida, Phys. Rev. D 81, 104004 (2010).

    ADS  Google Scholar 

  202. S. Chandrasekhar, Proc. R. Soc. London, Ser. A 392, 1 (1984).

    MathSciNet  ADS  Google Scholar 

  203. S.A. Teukolsky, Phys. Rev. Lett. 29, 1114 (1972).

    ADS  Google Scholar 

  204. E. Berti, V. Cardoso, M. Casals, Phys. Rev. D 73, 024013 (2006).

    MathSciNet  ADS  Google Scholar 

  205. S.A. Teukolsky, W.H. Press, Astrophys. J. 193, 443 (1974).

    ADS  Google Scholar 

  206. E.W. Leaver, Proc. R. Soc. London A 402, 285 (1985).

    MathSciNet  ADS  Google Scholar 

  207. W.H. Press, S.A. Teukolsky, Nature 238, 211 (1972).

    ADS  Google Scholar 

  208. J.M. Bardeen, Nature 226, 64 (1970).

    ADS  Google Scholar 

  209. R. Wald, Ann. Phys. 82, 548 (1974).

    ADS  Google Scholar 

  210. A.R. King, J.E. Pringle, J.A. Hofmann, Mon. Not. R. Astron. Soc. 385, 1621 (2008).

    ADS  Google Scholar 

  211. L.W. Brenneman, C.S. Reynolds, Astrophys. J. 652, 1028 (2006).

    ADS  Google Scholar 

  212. U. Sperhake et al., Phys. Rev. Lett. 103, 131102 (2009).

    ADS  Google Scholar 

  213. E. Berti, M. Volonteri, Astrophys. J. 684, 822 (2008).

    ADS  Google Scholar 

  214. L. Rezzolla, E.N. Dorband, C. Reisswig, P. Diener, D. Pollney, E. Schnetter, B. Szilágyi, Astrophys. J. 679, 1422 (2008).

    ADS  Google Scholar 

  215. L. Rezzolla, E. Barausse, E.N. Dorband, D. Pollney, C. Reisswig, J. Seiler, S. Husa, Phys. Rev. D 78, 044002 (2008).

    ADS  Google Scholar 

  216. E. Barausse, L. Rezzolla, Astrophys. J. Lett. 704, L40 (2009).

    ADS  Google Scholar 

  217. M. Kesden, G. Lockhart, E.S. Phinney, Phys. Rev. D 82, 124045 (2010).

    ADS  Google Scholar 

  218. M. Volonteri, P. Madau, E. Quataert, M.J. Rees, Astrophys. J. 620, 69 (2005).

    ADS  Google Scholar 

  219. A.R. King, U. Kolb, Mon. Not. R. Astron. Soc. 305, 654 (1999).

    ADS  Google Scholar 

  220. K. Belczynski, R.E. Taam, E. Rantsiou, M. van der Sluys, Astrophys. J. 682, 474 (2008).

    ADS  Google Scholar 

  221. G.B. Cook, S.L. Shapiro, S.A. Teukolsky, Astrophys. J. 424, 823 (1994).

    ADS  Google Scholar 

  222. E. Berti, N. Stergioulas, Mon. Not. R. Astron. Soc. 350, 1416 (2004).

    ADS  Google Scholar 

  223. B. Giacomazzo, L. Rezzolla, N. Stergioulas, Phys. Rev. D 84, 024022 (2011).

    ADS  Google Scholar 

  224. L. Baiotti, I. Hawke, P.J. Montero, F. Löffler, L. Rezzolla, N. Stergioulas, J.A. Font, E. Seidel, Phys. Rev. D 71, 024035 (2005).

    ADS  Google Scholar 

  225. S.R. Dolan, Phys. Rev. D 82, 104003 (2010).

    ADS  Google Scholar 

  226. B. Carter, Phys. Rev. 174, 1559 (1968).

    ADS  MATH  Google Scholar 

  227. D. Psaltis, D. Perrodin, K.R. Dienes, I. Mocioiu, Phys. Rev. Lett. 100, 091101 (2008).

    MathSciNet  ADS  Google Scholar 

  228. E. Barausse, T.P. Sotiriou, Phys. Rev. Lett. 101, 099001 (2008).

    ADS  Google Scholar 

  229. T.P. Sotiriou, V. Faraoni, Rev. Mod. Phys. 82, 451 (2010).

    MathSciNet  ADS  MATH  Google Scholar 

  230. D. Wands, Class. Quantum Grav. 11, 269 (1994).

    MathSciNet  ADS  Google Scholar 

  231. C.M. Will, H.W. Zaglauer, Astrophys. J. 346, 366 (1989).

    ADS  Google Scholar 

  232. L. Brenneman, C. Reynolds, M. Nowak, R. Reis, M. Trippe et al., Astrophys. J. 736, 103 (2011).

    ADS  Google Scholar 

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  1. CENTRA, Departamento de Física, Instituto Superior Técnico, Universidade Técnica de Lisboa - UTL, Av. Rovisco Pais 1, 1049, Lisboa, Portugal

    P. Pani

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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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