Applications of black hole perturbation theory

From the gauge/string duality to high-energy astrophysics
Regular Article

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.

References

  1. 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. 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.MathSciNetADSGoogle Scholar
  3. 3.
    M. Cavaglia, Int. J. Mod. Phys. A 18, 1843 (2003).MathSciNetADSMATHGoogle Scholar
  4. 4.
    J.M. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998).MathSciNetADSMATHGoogle Scholar
  5. 5.
    G.T. Horowitz, J. Polchinski, Gauge/gravity duality, gr-qc/0602037 (2006).Google Scholar
  6. 6.
    S.A. Hartnoll, Class. Quantum Grav. 26, 224002 (2009).MathSciNetADSGoogle Scholar
  7. 7.
    T. Regge, J.A. Wheeler, Phys. Rev. 108, 1063 (1957).MathSciNetADSMATHGoogle Scholar
  8. 8.
    F.J. Zerilli, Phys. Rev. D 2, 2141 (1970).MathSciNetADSMATHGoogle Scholar
  9. 9.
    C.V. Vishveshwara, Phys. Rev. D 1, 2870 (1970).ADSGoogle Scholar
  10. 10.
    H.-P. Nollert, Class. Quantum Grav. 16, R159 (1999).MathSciNetADSMATHGoogle Scholar
  11. 11.
    K.D. Kokkotas, B.G. Schmidt, Living Rev. Relativ. 2, 2 (1999).MathSciNetADSGoogle Scholar
  12. 12.
    E. Berti, V. Cardoso, A.O. Starinets, Class. Quantum Grav. 26, 163001 (2009).MathSciNetADSGoogle Scholar
  13. 13.
    R. Konoplya, A. Zhidenko, Rev. Mod. Phys. 83, 793 (2011).ADSGoogle Scholar
  14. 14.
    P. Pani, V. Cardoso, E. Berti, J. Read, M. Salgado, Phys. Rev. D 83, 081501 (2011).ADSGoogle Scholar
  15. 15.
    F. Pretorius, Phys. Rev. Lett. 95, 121101 (2005).MathSciNetADSGoogle Scholar
  16. 16.
    M. Campanelli, C.O. Lousto, P. Marronetti, Y. Zlochower, Phys. Rev. Lett. 96, 111101 (2006).ADSGoogle Scholar
  17. 17.
    F. Echeverria, Phys. Rev. D 40, 3194 (1989).ADSGoogle Scholar
  18. 18.
    J.D. Bekenstein, Phys. Rev. Lett. 28, 452 (1972).ADSGoogle Scholar
  19. 19.
    E. Berti, V. Cardoso, C.M. Will, Phys. Rev. D 73, 064030 (2006).MathSciNetADSGoogle Scholar
  20. 20.
    P.K. Kovtun, A.O. Starinets, Phys. Rev. D 72, 086009 (2005).ADSGoogle Scholar
  21. 21.
    D.T. Son, A.O. Starinets, Ann. Rev. Nucl. Part. Sci. 57, 95 (2007).ADSGoogle Scholar
  22. 22.
    S.K. Blau, Phys. Today 58, 23 (2005).ADSGoogle Scholar
  23. 23.
    C.P. Herzog, J. Phys. A 42, 343001 (2009).MathSciNetGoogle Scholar
  24. 24.
    S.A. Hartnoll, C.P. Herzog, G.T. Horowitz, Phys. Rev. Lett. 101, 031601 (2008).ADSGoogle Scholar
  25. 25.
    F. Benini, C.P. Herzog, R. Rahman, A. Yarom, JHEP 11, 2010 (137).Google Scholar
  26. 26.
    D.T. Son, Phys. Rev. D 78, 046003 (2008).MathSciNetADSGoogle Scholar
  27. 27.
    S.A. Hartnoll, J. Polchinski, E. Silverstein, D. Tong, JHEP 04, 2010 (120).Google Scholar
  28. 28.
    C.M. Will, Living Rev. Relativ. 9, 3 (2005).ADSGoogle Scholar
  29. 29.
    A. Abramovici et al., Science 256, 325 (1992).ADSGoogle Scholar
  30. 30.
    C.B.M.H. Chirenti, L. Rezzolla, Class. Quantum Grav. 24, 4191 (2007).MathSciNetADSMATHGoogle Scholar
  31. 31.
    S. Alexander, N. Yunes, Phys. Rep. 480, 1 (2009).MathSciNetADSGoogle Scholar
  32. 32.
    B. Zwiebach, Phys. Lett. B 156, 315 (1985).ADSGoogle Scholar
  33. 33.
    V. Cardoso, S. Chakrabarti, P. Pani, E. Berti, L. Gualtieri, Phys. Rev. Lett. 107, 241101 (2011).ADSGoogle Scholar
  34. 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).ADSGoogle Scholar
  35. 35.
    M. Visser, D.L. Wiltshire, Class. Quantum Grav. 21, 1135 (2004).MathSciNetADSMATHGoogle Scholar
  36. 36.
    E.G. Gimon, P. Horava, Phys. Lett. B 672, 299 (2009).MathSciNetADSGoogle Scholar
  37. 37.
    P. Amaro-Seoane et al., Class. Quantum Grav. 24, R113 (2007).MathSciNetADSMATHGoogle Scholar
  38. 38.
    D. Mateos, Class. Quantum Grav. 24, S713 (2007).MathSciNetADSMATHGoogle Scholar
  39. 39.
    S. Sachdev, M. Mueller, J. Phys.: Condens. Matter 21, 2009 (164216).Google Scholar
  40. 40.
    J. McGreevy, Holographic duality with a view toward many-body physics, arXiv:0909.0518v3 [hep-th] (2009).
  41. 41.
    D.T. Son, A.O. Starinets, JHEP 09, 042 (2002).MathSciNetADSGoogle Scholar
  42. 42.
    G.W. Gibbons, K.-i. Maeda, Nucl. Phys. B 298, 741 (1988).MathSciNetADSGoogle Scholar
  43. 43.
    D. Garfinkle, G.T. Horowitz, A. Strominger, Phys. Rev. D 43, 3140 (1991).MathSciNetADSGoogle Scholar
  44. 44.
    S. Monni, M. Cadoni, Nucl. Phys. B 466, 101 (1996).MathSciNetADSMATHGoogle Scholar
  45. 45.
    M.J. Duff, J.T. Liu, Nucl. Phys. B 554, 237 (1999).MathSciNetADSMATHGoogle Scholar
  46. 46.
    S.S. Gubser, F.D. Rocha, Phys. Rev. D 81, 046001 (2010).MathSciNetADSGoogle Scholar
  47. 47.
    P. Breitenlohner, D.Z. Freedman, Phys. Lett. B 115, 197 (1982).MathSciNetADSGoogle Scholar
  48. 48.
    G. Dotti, R.J. Gleiser, Class. Quantum Grav. 22, L1 (2005).MathSciNetADSMATHGoogle Scholar
  49. 49.
    M. Cadoni, G. D’Appollonio, P. Pani, JHEP 03, 100 (2010).MathSciNetADSGoogle Scholar
  50. 50.
    S.A. Hartnoll, C.P. Herzog, G.T. Horowitz, JHEP 12, 015 (2008).MathSciNetADSGoogle Scholar
  51. 51.
    K. Maeda, M. Natsuume, T. Okamura, Phys. Rev. D 79, 126004 (2009).ADSGoogle Scholar
  52. 52.
    G.T. Horowitz, J.E. Santos, D. Tong, Optical Conductivity with Holographic Lattices, arXiv:1204.0519v1 [hep-th] (2012).
  53. 53.
    S.S. Gubser, F.D. Rocha, Phys. Rev. Lett. 102, 061601 (2009).MathSciNetADSGoogle Scholar
  54. 54.
    T. Albash, C.V. Johnson, JHEP 09, 121 (2008).MathSciNetADSGoogle Scholar
  55. 55.
    O. Domenech, M. Montull, A. Pomarol, A. Salvio, P.J. Silva, JHEP 08, 033 (2010).ADSGoogle Scholar
  56. 56.
    M. Cadoni, P. Pani, JHEP 1104, 049 (2011).ADSGoogle Scholar
  57. 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. 58.
    G.T. Horowitz, Introduction to Holographic Superconductors, arXiv:1002.1722v2 [hep-th] (2010).
  59. 59.
    S.A. Hartnoll, P. Kovtun, Phys. Rev. D 76, 066001 (2007).ADSGoogle Scholar
  60. 60.
    S.A. Hartnoll, C.P. Herzog, Phys. Rev. D 76, 106012 (2007).MathSciNetADSGoogle Scholar
  61. 61.
    K. Goldstein et al., JHEP 10, 2010 (027).Google Scholar
  62. 62.
    M. Cadoni, S. Mignemi, M. Serra, Phys. Rev. D 84, 084046 (2011).ADSGoogle Scholar
  63. 63.
    M. Cadoni, P. Pani, M. Serra, JHEP 01, 091 (2010).MathSciNetADSGoogle Scholar
  64. 64.
    E. Berti, V. Cardoso, P. Pani, Phys. Rev. D 79, 101501 (2009).MathSciNetADSGoogle Scholar
  65. 65.
    G.T. Horowitz, V.E. Hubeny, Phys. Rev. D 62, 024027 (2000).MathSciNetADSGoogle Scholar
  66. 66.
    T. Harmark, J. Natario, R. Schiappa, Adv. Theor. Math. Phys. 14, 2010 (727).Google Scholar
  67. 67.
    S. Chandrasekhar, V. Ferrari, Proc. R. Soc. London A 434, 449 (1992).MathSciNetADSGoogle Scholar
  68. 68.
    S. Chandrasekhar, V. Ferrari, Proc. R. Soc. London A 437, 133 (1992).MathSciNetADSGoogle Scholar
  69. 69.
    J. Grain, A. Barrau, Nucl. Phys. B 742, 253 (2006).ADSMATHGoogle Scholar
  70. 70.
    G. Festuccia, H. Liu, A Bohr-Sommerfeld quantization formula for quasinormal frequencies of AdS black holes, arXiv:0811.1033v2 [gr-qc] (2008).
  71. 71.
    R.G. Daghigh, M.D. Green, Class. Quantum Grav. 26, 2009 (125017).Google Scholar
  72. 72.
    V. Cardoso, J.P.S. Lemos, Phys. Rev. D 64, 084017 (2001).MathSciNetADSGoogle Scholar
  73. 73.
    I.G. Moss, J.P. Norman, Class. Quantum Grav. 19, 2323 (2002).MathSciNetADSMATHGoogle Scholar
  74. 74.
    G. Michalogiorgakis, S.S. Pufu, JHEP 02, 023 (2007).MathSciNetADSGoogle Scholar
  75. 75.
    I. Bakas, JHEP 01, 003 (2009).MathSciNetADSGoogle Scholar
  76. 76.
    J.V. Rocha, JHEP 08, 075 (2008).MathSciNetADSGoogle Scholar
  77. 77.
    R.A. Konoplya, Phys. Rev. D 66, 044009 (2002).MathSciNetADSGoogle Scholar
  78. 78.
    V. Cardoso, O.J.C. Dias, Phys. Rev. D 70, 084011 (2004).MathSciNetADSGoogle Scholar
  79. 79.
    E. Berti, K.D. Kokkotas, Phys. Rev. D 67, 064020 (2003).MathSciNetADSGoogle Scholar
  80. 80.
    V. Cardoso, O.J.C. Dias, S. Yoshida, Phys. Rev. D 74, 044008 (2006).ADSGoogle Scholar
  81. 81.
    G. Gamow, Z. Phys. 51, 204 (1928).ADSMATHGoogle Scholar
  82. 82.
    S.A. Gurvitz, Phys. Rev. A 38, 1747 (1988).ADSGoogle Scholar
  83. 83.
    B. Wang, C.-Y. Lin, C. Molina, Phys. Rev. D 70, 064025 (2004).MathSciNetADSGoogle Scholar
  84. 84.
    P. Pani, V. Cardoso, L. Gualtieri, E. Berti, A. Ishibashi, in preparation (2012).Google Scholar
  85. 85.
    C. Hoyle, D. Kapner, B. Heckel, E. Adelberger, J. Gundlach, U. Schmidt, H. Swanson, Phys. Rev. D 70, 042004 (2004).ADSGoogle Scholar
  86. 86.
    S. Hawking, R. Penrose, The Nature of Space and Time: With a New Afterword by the Authors (Princeton University Press, Oxford, 2010).Google Scholar
  87. 87.
    A.G. Riess et al., Astron. J. 116, 1009 (1998).ADSGoogle Scholar
  88. 88.
    S. Perlmutter et al., Astrophys. J. 517, 565 (1999).ADSGoogle Scholar
  89. 89.
    D.N. Spergel et al., Astrophys. J. Suppl. 170, 377 (2007).ADSGoogle Scholar
  90. 90.
    S.M. Carroll, Living Rev. Relativ. 4, 1 (2001).ADSGoogle Scholar
  91. 91.
    P.J.E. Peebles, B. Ratra, Rev. Mod. Phys. 75, 559 (2003).MathSciNetADSMATHGoogle Scholar
  92. 92.
    A. Dekel, F. Stoehr, G.A. Mamon, T.J. Cox, J.R. Primack, Nature 437, 707 (2005).ADSGoogle Scholar
  93. 93.
    T. Clifton, P.G. Ferreira, A. Padilla, C. Skordis, Phys. Rep. 513, 1 (2012).MathSciNetADSGoogle Scholar
  94. 94.
    C. Brans, R.H. Dicke, Phys. Rev. 124, 925 (1961).MathSciNetADSMATHGoogle Scholar
  95. 95.
    A.D.F. Shinji Tsujikawa, Living Rev. Relativ. 13, 3 (2010).ADSGoogle Scholar
  96. 96.
    L. Blanchet, Living Rev. Relativ. 5, 3 (2002).ADSGoogle Scholar
  97. 97.
    D. Psaltis, Living Rev. Relativ. 11, 9 (2008).ADSGoogle Scholar
  98. 98.
    P. Pani, V. Cardoso, Phys. Rev. D 79, 084031 (2009).MathSciNetADSGoogle Scholar
  99. 99.
    C. Molina, P. Pani, V. Cardoso, L. Gualtieri, Phys. Rev. D 81, 124021 (2010).ADSGoogle Scholar
  100. 100.
    P. Pani, V. Cardoso, T. Delsate, Phys. Rev. Lett. 107, 031101 (2011).ADSGoogle Scholar
  101. 101.
    J. Casanellas, P. Pani, I. Lopes, V. Cardoso, Astrophys. J. 745, 15 (2012).ADSGoogle Scholar
  102. 102.
    P. Pani, E. Berti, V. Cardoso, J. Read, Phys. Rev. D 84, 104035 (2011).ADSGoogle Scholar
  103. 103.
    P. Pani, T. Delsate, V. Cardoso, Phys. Rev. D 85, 084020 (2012).ADSGoogle Scholar
  104. 104.
    B. Caron et al., Class. Quantum Grav. 14, 1461 (1997).ADSGoogle Scholar
  105. 105.
    E. Berti, A. Buonanno, C.M. Will, Phys. Rev. D 71, 084025 (2005).ADSGoogle Scholar
  106. 106.
    C.M. Will, N. Yunes, Class. Quantum Grav. 21, 4367 (2004).ADSMATHGoogle Scholar
  107. 107.
    R. Ruffini, J. Wheeler, Phys. Today 24, 30 (1971).ADSGoogle Scholar
  108. 108.
    B. Carter, Phys. Rev. Lett. 26, 331 (1971).ADSGoogle Scholar
  109. 109.
    R.M. Wald, Phys. Rev. Lett. 26, 1653 (1971).ADSGoogle Scholar
  110. 110.
    D.C. Robinson, Phys. Rev. Lett. 34, 905 (1975).ADSGoogle Scholar
  111. 111.
    J.D. Bekenstein, Phys. Rev. D 5, 1239 (1972).MathSciNetADSGoogle Scholar
  112. 112.
    P. Bizon, Phys. Rev. Lett. 64, 2844 (1990).MathSciNetADSMATHGoogle Scholar
  113. 113.
    S. Droz, M. Heusler, N. Straumann, Phys. Lett. B 268, 371 (1991).MathSciNetADSGoogle Scholar
  114. 114.
    S.S. Gubser, Class. Quantum Grav. 22, 5121 (2005).MathSciNetADSMATHGoogle Scholar
  115. 115.
    S.S. Gubser, Phys. Rev. Lett. 101, 191601 (2008).MathSciNetADSGoogle Scholar
  116. 116.
    S.S. Gubser, Phys. Rev. D 78, 065034 (2008).ADSGoogle Scholar
  117. 117.
    S.B. Giddings, S.D. Thomas, Phys. Rev. D 65, 056010 (2002).ADSGoogle Scholar
  118. 118.
    P. Kanti, Int. J. Mod. Phys. A 19, 4899 (2004).MathSciNetADSMATHGoogle Scholar
  119. 119.
    P. Kanti, Lect. Notes Phys. 769, 387 (2009).MathSciNetADSGoogle Scholar
  120. 120.
    G.W. Gibbons, Commun. Math. Phys. 44, 245 (1975).MathSciNetADSGoogle Scholar
  121. 121.
    J.D. Bekenstein, Phys. Rev. D 51, 6608 (1995).MathSciNetADSGoogle Scholar
  122. 122.
    J.R. Oppenheimer, H. Snyder, Phys. Rev. 56, 455 (1939).ADSMATHGoogle Scholar
  123. 123.
    R. Penrose, Phys. Rev. Lett. 14, 57 (1965).MathSciNetADSMATHGoogle Scholar
  124. 124.
    R.H. Price, Phys. Rev. D 5, 2439 (1972).MathSciNetADSGoogle Scholar
  125. 125.
    R. Penrose, Riv. Nuovo Cimento 1, 252 (1969).Google Scholar
  126. 126.
    I. Hauser, F. Ernst, J. Math. Phys. 22, 1051 (1981).MathSciNetADSMATHGoogle Scholar
  127. 127.
    F.D. Ryan, Phys. Rev. D 52, 5707 (1995).ADSGoogle Scholar
  128. 128.
    P. Pani, C.F. Macedo, L.C. Crispino, V. Cardoso, Phys. Rev. D 84, 087501 (2011).ADSGoogle Scholar
  129. 129.
    N. Yunes, L.C. Stein, Phys. Rev. D 83, 104002 (2011).ADSGoogle Scholar
  130. 130.
    B.A. Campbell, N. Kaloper, K.A. Olive, Phys. Lett. B 285, 199 (1992).MathSciNetADSGoogle Scholar
  131. 131.
    S. Mignemi, N. Stewart, Phys. Lett. B 298, 299 (1993).ADSGoogle Scholar
  132. 132.
    P. Kanti, N.E. Mavromatos, J. Rizos, K. Tamvakis, E. Winstanley, Phys. Rev. D 54, 5049 (1996).MathSciNetADSGoogle Scholar
  133. 133.
    T. Torii, H. Yajima, K.-i. Maeda, Phys. Rev. D 55, 739 (1997).MathSciNetADSGoogle Scholar
  134. 134.
    B. Kleihaus, J. Kunz, E. Radu, Phys. Rev. Lett. 106, 151104 (2011).ADSGoogle Scholar
  135. 135.
    N. Yunes, F. Pretorius, Phys. Rev. D 79, 084043 (2009).ADSGoogle Scholar
  136. 136.
    K. Konno, T. Matsuyama, S. Tanda, Prog. Theor. Phys. 122, 561 (2009).ADSMATHGoogle Scholar
  137. 137.
    N. Yunes, C.F. Sopuerta, Phys. Rev. D 77, 064007 (2008).MathSciNetADSGoogle Scholar
  138. 138.
    E. Barausse, T.P. Sotiriou, Phys. Rev. Lett. 101, 099001 (2008).ADSGoogle Scholar
  139. 139.
    V. Cardoso, L. Gualtieri, Phys. Rev. D 80, 064008 (2009).ADSGoogle Scholar
  140. 140.
    P. Pani, V. Cardoso, L. Gualtieri, Phys. Rev. D 83, 104048 (2011).ADSGoogle Scholar
  141. 141.
    E. Berti, J. Cardoso, V. Cardoso, M. Cavaglia, Phys. Rev. D 76, 104044 (2007).ADSGoogle Scholar
  142. 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. 143.
    Z.-K. Guo, N. Ohta, T. Torii, Prog. Theor. Phys. 120, 581 (2008).ADSMATHGoogle Scholar
  144. 144.
    K.-i. Maeda, N. Ohta, Y. Sasagawa, Phys. Rev. D 80, 104032 (2009).MathSciNetADSGoogle Scholar
  145. 145.
    S. Mignemi, N.R. Stewart, Phys. Rev. D 47, 5259 (1993).MathSciNetADSGoogle Scholar
  146. 146.
    P. Kanti, N.E. Mavromatos, J. Rizos, K. Tamvakis, E. Winstanley, Phys. Rev. D 57, 6255 (1998).MathSciNetADSGoogle Scholar
  147. 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. 148.
    D. Psaltis, Probes and Tests of Strong-Field Gravity with Observations in the Electromagnetic Spectrum, arXiv:0806.1531 [astro-ph] (2008).
  149. 149.
    M. Visser, PoS BHS GR and strings, 001 (2008).Google Scholar
  150. 150.
    M.A. Abramowicz, W. Kluzniak, J.-P. Lasota, Astron. Astrophys. 396, L31 (2002).ADSMATHGoogle Scholar
  151. 151.
    F.E. Schunck, E.W. Mielke, Class. Quantum Grav. 20, R301 (2003).MathSciNetADSMATHGoogle Scholar
  152. 152.
    D.F. Torres, S. Capozziello, G. Lambiase, Phys. Rev. D 62, 104012 (2000).ADSGoogle Scholar
  153. 153.
    F.S. Guzman, Phys. Rev. D 73, 021501 (2006).ADSGoogle Scholar
  154. 154.
    M. Kesden, J. Gair, M. Kamionkowski, Phys. Rev. D 71, 044015 (2005).ADSGoogle Scholar
  155. 155.
    S. Yoshida, Y. Eriguchi, T. Futamase, Phys. Rev. D 50, 6235 (1994).ADSGoogle Scholar
  156. 156.
    J. Balakrishna, R. Bondarescu, G. Daues, F. Siddhartha Guzman, E. Seidel, Class. Quantum Grav. 23, 2631 (2006).MathSciNetADSMATHGoogle Scholar
  157. 157.
    E. Berti, V. Cardoso, Int. J. Mod. Phys. D 15, 2209 (2006).MathSciNetADSMATHGoogle Scholar
  158. 158.
    P.O. Mazur, E. Mottola, Gravitational condensate stars, arXiv:gr-qc/0109035v5 (2001).
  159. 159.
    G. Chapline, E. Hohlfeld, R.B. Laughlin, D.I. Santiago, Int. J. Mod. Phys. A 18, 3587 (2003).ADSGoogle Scholar
  160. 160.
    P.O. Mazur, E. Mottola, Proc. Natl. Acad. Sci. U.S.A. 101, 9545 (2004).ADSGoogle Scholar
  161. 161.
    W. Israel, Nuovo Cimento B 44, Suppl. 10, 1 (1966).Google Scholar
  162. 162.
    J.L. Friedman, Commun. Math. Phys. 63, 243 (1978).ADSMATHGoogle Scholar
  163. 163.
    B.F. Schutz, N. Comins, Mon. Not. R. Astron. Soc. 182, 69 (1978).ADSGoogle Scholar
  164. 164.
    Y. Zel’dovich, Zh. Eksp. Teor. Fiz. 14, 270 (1971) and Zh. Eksp. Teor. Fiz. 62.Google Scholar
  165. 165.
    C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (W.H. Freeman, San Francisco, 1973) ISBN 978-0-7167-0344-0.Google Scholar
  166. 166.
    V. Cardoso, P. Pani, M. Cadoni, M. Cavaglia, Phys. Rev. D 77, 124044 (2008).ADSGoogle Scholar
  167. 167.
    V. Cardoso, P. Pani, M. Cadoni, M. Cavaglia, Class. Quantum Grav. 25, 195010 (2008).MathSciNetADSGoogle Scholar
  168. 168.
    P. Pani, V. Cardoso, M. Cadoni, M. Cavaglia, PoS BHS GR and strings, 027 (2008).Google Scholar
  169. 169.
    C.B.M.H. Chirenti, L. Rezzolla, Phys. Rev. D 78, 084011 (2008).ADSGoogle Scholar
  170. 170.
    P.P. Fiziev, Class. Quantum Grav. 23, 2447 (2006).MathSciNetADSMATHGoogle Scholar
  171. 171.
    P. Pani, E. Berti, V. Cardoso, Y. Chen, R. Norte, Phys. Rev. D 80, 124047 (2009).ADSGoogle Scholar
  172. 172.
    M. Visser, Lorentzian Wormholes: From Einstein to Hawking (AIP, Woodbury, 1995) p. 412.Google Scholar
  173. 173.
    E. Poisson, M. Visser, Phys. Rev. D 52, 7318 (1995).MathSciNetADSGoogle Scholar
  174. 174.
    N. Andersson, Y. Kojima, K.D. Kokkotas, Astrophys. J. 462, 855 (1996).ADSGoogle Scholar
  175. 175.
    K.D. Kokkotas, B.F. Schutz, Gen. Relativ. Gravit. 18, 913 (1986).ADSMATHGoogle Scholar
  176. 176.
    N. Andersson, Gen. Relativ. Gravit. 28, 1433 (1996).ADSMATHGoogle Scholar
  177. 177.
    M. Leins, H.P. Nollert, M.H. Soffel, Phys. Rev. D 48, 3467 (1993).ADSGoogle Scholar
  178. 178.
    E. Berti, Gravitational waves from perturbed stars, PhD thesis.Google Scholar
  179. 179.
    S. Chandrasekhar, V. Ferrari, Proc. R. Soc. London A 432, 247 (1991).MathSciNetADSGoogle Scholar
  180. 180.
    Y. Kojima, Prog. Theor. Phys. 77, 297 (1987).ADSGoogle Scholar
  181. 181.
    L. Gualtieri, E. Berti, J.A. Pons, G. Miniutti, V. Ferrari, Phys. Rev. D 64, 104007 (2001).ADSGoogle Scholar
  182. 182.
    J.A. Pons, E. Berti, L. Gualtieri, G. Miniutti, V. Ferrari, Phys. Rev. D 65, 104021 (2002).ADSGoogle Scholar
  183. 183.
    E. Berti, J.A. Pons, G. Miniutti, L. Gualtieri, V. Ferrari, Phys. Rev. D 66, 064013 (2002).ADSGoogle Scholar
  184. 184.
    P. Pani, E. Barausse, E. Berti, V. Cardoso, Phys. Rev. D 82, 044009 (2010).ADSGoogle Scholar
  185. 185.
    E. Poisson, Phys. Rev. D 47, 1497 (1993).MathSciNetADSGoogle Scholar
  186. 186.
    C. Cutler, E. Poisson, G.J. Sussman, L.S. Finn, Phys. Rev. D 47, 1511 (1993).MathSciNetADSGoogle Scholar
  187. 187.
    C. Cutler, D. Kennefick, E. Poisson, Phys. Rev. D 50, 3816 (1994).ADSGoogle Scholar
  188. 188.
    E. Poisson, Phys. Rev. D 52, 5719 (1995).MathSciNetADSGoogle Scholar
  189. 189.
    E.E. Flanagan, T. Hinderer, Phys. Rev. D 77, 021502 (2008).ADSGoogle Scholar
  190. 190.
    N. Yunes, E. Berti, Phys. Rev. D 77, 124006 (2008).ADSGoogle Scholar
  191. 191.
    K.D. Kokkotas, J. Ruoff, N. Andersson, Phys. Rev. D 70, 043003 (2004).ADSGoogle Scholar
  192. 192.
    T. Damour, S.N. Solodukhin, Phys. Rev. D 76, 024016 (2007).MathSciNetADSGoogle Scholar
  193. 193.
    G. Dotti, R. Gleiser, J. Pullin, Phys. Lett. B 644, 289 (2007).ADSMATHGoogle Scholar
  194. 194.
    G. Dotti, R.J. Gleiser, I.F. Ranea-Sandoval, H. Vucetich, Class. Quantum Grav. 25, 245012 (2008).MathSciNetADSGoogle Scholar
  195. 195.
    K. Hioki, K.-i. Maeda, Phys. Rev. D 80, 024042 (2009).ADSGoogle Scholar
  196. 196.
    C. Bambi, N. Yoshida, Class. Quantum Grav. 27, 205006 (2010).MathSciNetADSGoogle Scholar
  197. 197.
    C. Reina, A. Treves, Astrophys. J. 227, 596 (1979).ADSGoogle Scholar
  198. 198.
    C. Bambi, K. Freese, T. Harada, R. Takahashi, N. Yoshida, Phys. Rev. D 80, 104023 (2009).ADSGoogle Scholar
  199. 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. 200.
    R. Takahashi, T. Harada, Class. Quantum Grav. 27, 075003 (2010).MathSciNetADSGoogle Scholar
  201. 201.
    C. Bambi, T. Harada, R. Takahashi, N. Yoshida, Phys. Rev. D 81, 104004 (2010).ADSGoogle Scholar
  202. 202.
    S. Chandrasekhar, Proc. R. Soc. London, Ser. A 392, 1 (1984).MathSciNetADSGoogle Scholar
  203. 203.
    S.A. Teukolsky, Phys. Rev. Lett. 29, 1114 (1972).ADSGoogle Scholar
  204. 204.
    E. Berti, V. Cardoso, M. Casals, Phys. Rev. D 73, 024013 (2006).MathSciNetADSGoogle Scholar
  205. 205.
    S.A. Teukolsky, W.H. Press, Astrophys. J. 193, 443 (1974).ADSGoogle Scholar
  206. 206.
    E.W. Leaver, Proc. R. Soc. London A 402, 285 (1985).MathSciNetADSGoogle Scholar
  207. 207.
    W.H. Press, S.A. Teukolsky, Nature 238, 211 (1972).ADSGoogle Scholar
  208. 208.
    J.M. Bardeen, Nature 226, 64 (1970).ADSGoogle Scholar
  209. 209.
    R. Wald, Ann. Phys. 82, 548 (1974).ADSGoogle Scholar
  210. 210.
    A.R. King, J.E. Pringle, J.A. Hofmann, Mon. Not. R. Astron. Soc. 385, 1621 (2008).ADSGoogle Scholar
  211. 211.
    L.W. Brenneman, C.S. Reynolds, Astrophys. J. 652, 1028 (2006).ADSGoogle Scholar
  212. 212.
    U. Sperhake et al., Phys. Rev. Lett. 103, 131102 (2009).ADSGoogle Scholar
  213. 213.
    E. Berti, M. Volonteri, Astrophys. J. 684, 822 (2008).ADSGoogle Scholar
  214. 214.
    L. Rezzolla, E.N. Dorband, C. Reisswig, P. Diener, D. Pollney, E. Schnetter, B. Szilágyi, Astrophys. J. 679, 1422 (2008).ADSGoogle Scholar
  215. 215.
    L. Rezzolla, E. Barausse, E.N. Dorband, D. Pollney, C. Reisswig, J. Seiler, S. Husa, Phys. Rev. D 78, 044002 (2008).ADSGoogle Scholar
  216. 216.
    E. Barausse, L. Rezzolla, Astrophys. J. Lett. 704, L40 (2009).ADSGoogle Scholar
  217. 217.
    M. Kesden, G. Lockhart, E.S. Phinney, Phys. Rev. D 82, 124045 (2010).ADSGoogle Scholar
  218. 218.
    M. Volonteri, P. Madau, E. Quataert, M.J. Rees, Astrophys. J. 620, 69 (2005).ADSGoogle Scholar
  219. 219.
    A.R. King, U. Kolb, Mon. Not. R. Astron. Soc. 305, 654 (1999).ADSGoogle Scholar
  220. 220.
    K. Belczynski, R.E. Taam, E. Rantsiou, M. van der Sluys, Astrophys. J. 682, 474 (2008).ADSGoogle Scholar
  221. 221.
    G.B. Cook, S.L. Shapiro, S.A. Teukolsky, Astrophys. J. 424, 823 (1994).ADSGoogle Scholar
  222. 222.
    E. Berti, N. Stergioulas, Mon. Not. R. Astron. Soc. 350, 1416 (2004).ADSGoogle Scholar
  223. 223.
    B. Giacomazzo, L. Rezzolla, N. Stergioulas, Phys. Rev. D 84, 024022 (2011).ADSGoogle Scholar
  224. 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).ADSGoogle Scholar
  225. 225.
    S.R. Dolan, Phys. Rev. D 82, 104003 (2010).ADSGoogle Scholar
  226. 226.
    B. Carter, Phys. Rev. 174, 1559 (1968).ADSMATHGoogle Scholar
  227. 227.
    D. Psaltis, D. Perrodin, K.R. Dienes, I. Mocioiu, Phys. Rev. Lett. 100, 091101 (2008).MathSciNetADSGoogle Scholar
  228. 228.
    E. Barausse, T.P. Sotiriou, Phys. Rev. Lett. 101, 099001 (2008).ADSGoogle Scholar
  229. 229.
    T.P. Sotiriou, V. Faraoni, Rev. Mod. Phys. 82, 451 (2010).MathSciNetADSMATHGoogle Scholar
  230. 230.
    D. Wands, Class. Quantum Grav. 11, 269 (1994).MathSciNetADSGoogle Scholar
  231. 231.
    C.M. Will, H.W. Zaglauer, Astrophys. J. 346, 366 (1989).ADSGoogle Scholar
  232. 232.
    L. Brenneman, C. Reynolds, M. Nowak, R. Reis, M. Trippe et al., Astrophys. J. 736, 103 (2011).ADSGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer 2012

Authors and Affiliations

  1. 1.CENTRA, Departamento de Física, Instituto Superior TécnicoUniversidade Técnica de Lisboa - UTLLisboaPortugal

Personalised recommendations