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Black holes in the presence of dark energy

 a,  b,  b
a Laboratoire de Physique Theorique d’Orsay CNRS UMR 8627, Université Paris-Sud 11, Bâtiment 210, Orsay Cedex, 91405, France
b Institute for Nuclear Research, Russian Academy of Sciences, prosp. 60-letiya Oktyabrya 7a, Moscow, 117312, Russian Federation

The new, rapidly developing field of theoretical research into dark energy interaction with black holes (and in particular, the accretion of dark energy onto black holes) is reviewed. The term “dark energy” is meant to cover a wide range of field theory models as well as perfect fluids with various equations of state, including cosmological dark energy. Various accretion models are analyzed in terms of the simplest test field approximation or by allowing for back-reaction on the black hole metric. The behavior of various types of dark energy in the vicinity of Schwarzschild and electrically charged black holes is examined. Nontrivial effects due to the presence of dark energy in the black hole vicinity are discussed. In particular, a physical explanation is given of why a black hole decreases in mass when accreting phantom energy, a process in which the basic energy conditions of the famous theorem of nondecreasing horizon area in classical black holes are violated. A theoretical possibility of a signal escaping from beneath the black hole event horizon is discussed for a number of dark energy models. Finally, the violation of the laws of thermodynamics by black holes in the presence of noncanonical fields is considered.

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Fulltext is also available at DOI: 10.3367/UFNe.0183.201312a.1257
PACS: 04.70.Bw, 04.70.Dy, 95.36.+x, 98.80.Cq (all)
DOI: 10.3367/UFNe.0183.201312a.1257
URL: https://ufn.ru/en/articles/2013/12/a/
000332531200001
2013PhyU...56.1153E
Citation: Babichev E O, Dokuchaev V I, Eroshenko Yu N "Black holes in the presence of dark energy" Phys. Usp. 56 1155–1175 (2013)
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Received: 25th, March 2013, revised: 7th, June 2013, 24th, June 2013

Îðèãèíàë: Áàáè÷åâ Å Î, Äîêó÷àåâ Â È, Åðîøåíêî Þ Í «×¸ðíûå äûðû â ïðèñóòñòâèè ò¸ìíîé ýíåðãèè» ÓÔÍ 183 1257–1280 (2013); DOI: 10.3367/UFNr.0183.201312a.1257

References (222) ↓ Cited by (64) Similar articles (20)

  1. Perlmutter S Usp. Fiz. Nauk 183 1060 (2013); Perlmutter S Rev. Mod. Phys. 84 1127 (2012)
  2. Shmidt B P Usp. Fiz. Nauk 183 1078 (2013); Schmidt B P Rev. Mod. Phys. 84 1151 (2012)
  3. Riss A Dzh Usp. Fiz. Nauk 183 1090 (2013); Riess A G Rev. Mod. Phys. 84 1165 (2012)
  4. Bahcall N A et al. Science 284 1481 (1999)
  5. Riess A G et al. Astron. J. 116 1009 (1998)
  6. Perlmutter S et al. Astrophys. J. 517 565 (1999)
  7. Bennett C L et al. Astrophys. J. Suppl. 148 1 (2003)
  8. Chernin A D Usp. Fiz. Nauk 178 267 (2008); Chernin A D Phys. Usp. 51 253 (2008)
  9. Chernin A D Usp. Fiz. Nauk 183 741 (2013); Chernin A D Phys. Usp. 56 704 (2013)
  10. Lukash V N, Rubakov V A Usp. Fiz. Nauk 178 301 (2008); Lukash V N, Rubakov V A Phys. Usp. 51 283 (2008)
  11. Bolotin Yu L, Erokhin D A, Lemets O A Usp. Fiz. Nauk 182 941 (2012); Bolotin Yu L, Erokhin D A, Lemets O A Phys. Usp. 55 876 (2012)
  12. Copeland E J, Sami M, Tsujikawa S Int. J. Mod. Phys. D 15 1753 (2006)
  13. Einstein A Sitzungsber. Königl. Preuß. Akad. Wissenschaft. Berlin 1 142 (1917); Einshtein A Sobranie Nauchnykh Trudov Vol. 1 (Pod red. I E Tamma, Ya A Smorodinskogo, B G Kuznetsova) (M.: Nauka, 1965) p. 601
  14. Einstein A Z. Phys. 11 326 (1922); Einshtein A Sobranie Nauchnykh Trudov Vol. 2 (Pod red. I E Tamma, Ya A Smorodinskogo, B G Kuznetsova) (M.: Nauka, 1966) p. 118; Einshtein A Usp. Fiz. Nauk 80 453 (1963)
  15. Einstein A Z. Phys. 16 228 (1922); Einshtein A Sobranie Nauchnykh Trudov Vol. 2 (Pod red. I E Tamma, Ya A Smorodinskogo, B G Kuznetsova) (M.: Nauka, 1966) p. 119; Einshtein A Usp. Fiz. Nauk 80 453 (1963)
  16. Friedmann A Z. Phys. 10 (1) 377 (1922); Fridman A Zhurn. Russk. Fiz.-khim. Obshch-va 56 59 (1924)
  17. Friedmann A Z. Phys. 21 (1) 326 (1924); Fridman A Usp. Fiz. Nauk 80 447 (1963)
  18. Cherepashchuk A M Usp. Fiz. Nauk 183 535 (2013); Cherepashchuk A M Phys. Usp. 56 509 (2013)
  19. Yoo J, Watanabe Y Int. J. Mod. Phys. D 21 1230002 (2012)
  20. Burdyuzha V V Usp. Fiz. Nauk 180 439 (2010); Burdyuzha V V Phys. Usp. 53 419 (2010)
  21. Wetterich C Nucl. Phys. B 302 668 (1988)
  22. Peebles P J E, Ratra B Astrophys. J. 325 L17 (1988)
  23. Ratra B, Peebles P J E Phys. Rev. D 37 3406 (1988)
  24. Frieman J A et al. Phys. Rev. Lett. 75 2077 (1995)
  25. Caldwell R R, Dave R, Steinhardt P J Phys. Rev. Lett. 80 1582 (1998)
  26. Zlatev I, Wang L, Steinhardt P J Phys. Rev. Lett. 82 896 (1999)
  27. Albrecht A, Skordis C Phys. Rev. Lett. 84 2076 (2000)
  28. Armendáriz-Picón C, Damour T, Mukhanov V Phys. Lett. B 458 209 (1999)
  29. Armendariz-Picon C, Mukhanov V, Steinhardt P J Phys. Rev. Lett. 85 4438 (2000)
  30. Chiba T, Okabe T, Yamaguchi M Phys. Rev. D 62 023511 (2000)
  31. Arkani-Hamed N et al. JHEP (05) 074 (2004)
  32. Nicolis A, Rattazzi R, Trincherini E Phys. Rev. D 79 064036 (2009)
  33. Deffayet C, Esposito-Farèse G, Vikman A Phys. Rev. D 79 084003 (2009)
  34. Deffayet C, Deser S, Esposito-Farèse G Phys. Rev. D 80 064015 (2009)
  35. Chow N, Khoury J Phys. Rev. D 80 024037 (2009)
  36. Sahni V, Starobinsky A Int. J. Mod. Phys. D 9 373 (2000)
  37. Maia M D, Monte E M, Maia J M F Phys. Lett. B 585 11 (2004)
  38. Jordan P Nature 164 637 (1949)
  39. Fierz M Helv. Phys. Acta 29 128 (1956)
  40. Brans C, Dicke R H Phys. Rev. 124 925 (1961)
  41. Damour T, Esposito-Farèse G Class. Quantum Grav. 9 2093 (1992)
  42. Sotiriou T P, Faraoni V Rev. Mod. Phys. 82 451 (2010)
  43. Rubakov V A Usp. Fiz. Nauk 171 913 (2001); Rubakov V A Phys. Usp. 44 871 (2001)
  44. De Felice A et al. Class. Quantum Grav. 30 184004 (2013); De Felice A et al. arXiv:1304.0484
  45. Rubakov V A, Tinyakov P G Usp. Fiz. Nauk 178 785 (2008); Rubakov V A, Tinyakov P G Phys. Usp. 51 759 (2008)
  46. Padmanabhan T, Choudhury T R Phys. Rev. D 66 081301(R) (2002)
  47. Clarkson C et al. Rep. Prog. Phys. 74 112901 (2011)
  48. Biermann P L, Harms B C arXiv:1305.0498
  49. Caldwell R R Phys. Lett. B 545 23 (2002)
  50. Caldwell R R, Kamionkowski M, Weinberg N N Phys. Rev. Lett. 91 071301 (2003)
  51. Ade P A R et al. (Planck Collab.) arXiv:1303.5076
  52. Carroll S M, Hoffman M, Trodden M Phys. Rev. D 68 023509 (2003)
  53. Cline J M, Jeon S, Moore G D Phys. Rev. D 70 043543 (2004)
  54. Rubakov V A Teor. Mat. Fiz. 149 409 (2006); Rubakov V A Theor. Math. Phys. 149 1651 (2006)
  55. Libanov M et al. JCAP (08) 010 (2007)
  56. Deffayet C et al. JCAP (10) 026 (2010)
  57. Volonteri M Astron. Astrophys. Rev. 18 279 (2010)
  58. Lukash V N, Mikheeva E V, Strokov V N Usp. Fiz. Nauk 182 216 (2012); Lukash V N, Mikheeva E V, Strokov V N Phys. Usp. 55 204 (2012)
  59. Hoyle F, Lyttleton R A Math. Proc. Cambr. Phil. Soc. 35 405 (1939)
  60. Bondi H, Hoyle F Mon. Not. R. Astron. Soc. 104 273 (1944)
  61. Bondi H Mon. Not. R. Astron. Soc. 112 195 (1952)
  62. Gaite J Astron. Astrophys. 449 861 (2006)
  63. Michel F C Astrophys. Space Sci. 15 153 (1972)
  64. Begelman M C Astron. Astrophys. 70 583 (1978)
  65. Ray D Astron. Astrophys. 82 368 (1980)
  66. Chang K M Astron. Astrophys. 142 212 (1985)
  67. Pandey U S Astrophys. Space Sci. 136 195 (1987)
  68. Petrich L I, Shapiro S L, Teukolsky S A Phys. Rev. Lett. 60 1781 (1988)
  69. Chakrabarti S K "Study of accretion processes on black holes: Fifty years of developments" Frontiers In Astrophysics (Ed. S K Chakrabarti) (New Delhi: Allied Publ., 2002) p. 145; Chakrabarti S K astro-ph/0402562
  70. Zel’dovich Ya B, Novikov I D Astron. Zhurn. 43 758 (1966); Zel’dovich Ya B, Novikov I D Sov. Astron. 10 602 (1967)
  71. Carr B J, Hawking S W Mon. Not. R. Astron. Soc. 168 399 (1974)
  72. Bicknell G V, Henriksen R N Astrophys. J. 225 237 (1978)
  73. Carr B J, Yahil A Astrophys. J. 360 330 (1990)
  74. Maeda H, Koga J, Maeda K Phys. Rev. D 66 087501 (2002)
  75. Thorne K S, Flammang R A, Zytkow A N Mon. Not. R. Astron. Soc. 194 475 (1981)
  76. Maeda H, Harada T, Carr B J Phys. Rev. D 77 024023 (2008)
  77. Harada T, Carr B Phys. Rev. D 72 044021 (2005)
  78. Bettwieser E, Glatzel W Astron. Astrophys. 94 306 (1981)
  79. Malec E Phys. Rev. D 60 104043 (1999)
  80. Shatskii A A, Andreev A Yu Zh. Eksp. Teor. Fiz. 116 353 (1999); Shatskii A A, Andreev A Yu JETP 89 189 (1999)
  81. Beskin V S, Par’ev V I Usp. Fiz. Nauk 163 (6) 95 (1993); Beskin V S, Par’ev V I Phys. Usp. 36 529 (1993)
  82. Beskin V S Usp. Fiz. Nauk 167 689 (1997); Beskin V S Phys. Usp. 40 659 (1997)
  83. Beskin V S Usp. Fiz. Nauk 173 1247 (2003); Beskin V S Phys. Usp. 46 1209 (2003)
  84. Beskin V S Osesimmetrichnye Statsionarnye Techeniya v Astrofizike (M.: Fizmatlit, 2005); Beskin V S MHD Flows In Compact Astrophysical Objects (Heidelberg: Springer, 2010)
  85. Babichev E, Dokuchaev V, Eroshenko Yu Phys. Rev. Lett. 93 021102 (2004)
  86. Babichev E O, Dokuchaev V I, Eroshenko Yu N Zh. Eksp. Teor. Fiz. 127 597 (2005); Babichev E O, Dokuchaev V I, Eroshenko Yu N JETP 100 528 (2005)
  87. Carr B J, Harada T, Maeda H Class. Quantum Grav. 27 183101 (2010)
  88. Pepe C, Pellizza L J, Romero G E Mon. Not. R. Astron. Soc. 420 3298 (2012)
  89. Jacobson T Phys. Rev. Lett. 83 2699 (1999)
  90. Frolov A V, Kofman L JCAP (05) 009 (2003)
  91. Unruh W G Phys. Rev. D 14 3251 (1976)
  92. Ureña-López L A, Liddle A R Phys. Rev. D 66 083005 (2002)
  93. Kuchiev M Yu, Flambaum V V Phys. Rev. D 70 044022 (2004)
  94. Cruz-Osorio A, Guzmán F S, Lora-Clavijo F D JCAP (06) 029 (2011)
  95. Guzmán F S, Lora-Clavijo F D Phys. Rev. D 85 024036 (2012)
  96. Frolov A V Phys. Rev. D 70 061501(R) (2004)
  97. Mukohyama S Phys. Rev. D 71 104019 (2005)
  98. Ford L H, Roman T A Phys. Rev. D 64 024023 (2001)
  99. Shatskii A A Zh. Eksp. Teor. Fiz. 131 851 (2007); Shatskii A A JETP 104 743 (2007)
  100. Landau L D, Lifshits E M Gidrodinamika (M.: Nauka, 1988); Landau L D, Lifshitz E M Fluid Mechanics (Oxford: Pergamon Press, 1987)
  101. Hawking S W, Ellis G F R The Large Scale Structure Of Space-Time (Cambridge: Univ. Press, 1973); Khoking S, Ellis Dzh Krupnomasshtabnaya Struktura Prostranstva-vremeni (M.: Mir, 1977)
  102. Rodrigues M G, Saa A Phys. Rev. D 80 104018 (2009)
  103. González J A, Guzmán F S Phys. Rev. D 79 121501(R) (2009)
  104. Lora-Clavijo F D, González J A, Guzmán F S AIP Conf. Proc. 1256 339 (2010)
  105. Shatskii A A i dr. Zh. Eksp. Teor. Fiz. 137 268 (2010); Shatskiy A A et al. JETP 110 235 (2010)
  106. Bonnor W B Gen. Relat. Grav. 21 1143 (1989)
  107. Shatskii A A, Novikov I D, Kardashev N S Usp. Fiz. Nauk 181 399 (2011); Shatskiy A A, Novikov I D, Kardashev N S Phys. Usp. 54 381 (2011)
  108. Ivanov P B Usp. Fiz. Nauk 182 1319 (2012); Ivanov P B Phys. Usp. 55 1232 (2012)
  109. Jiménez Madrid J A, González-Díaz P F Grav. Cosmol. 14 213 (2008)
  110. Jamil M, Qadir A, Rashid M A Eur. Phys. J. C 58 325 (2008)
  111. Babichev E O, Dokuchaev V I, Eroshenko Yu N Zh. Eksp. Teor. Fiz. 139 899 (2011); Babichev E O, Dokuchaev V I, Eroshenko Yu N JETP 112 784 (2011)
  112. Bardeen J M, Carter B, Hawking S W Commun. Math. Phys. 31 161 (1973)
  113. Sharif M, Abbas G Mod. Phys. Lett. A 26 1731 (2011)
  114. Babichev E et al. Phys. Rev. D 78 104027 (2008)
  115. Bambi C et al. Phys. Rev. D 80 104023 (2009)
  116. Babichev E, Mukhanov V, Vikman A JHEP (02) 101 (2008)
  117. Babichev E Phys. Rev. D 83 024008 (2011)
  118. Garriga J, Mukhanov V F Phys. Lett. B 458 219 (1999)
  119. Mukhanov V, Vikman A JCAP (02) 004 (2006)
  120. Armendariz-Picon C, Lim E A JCAP (08) 007 (2005)
  121. Rendall A D Class. Quantum Grav. 23 1557 (2006)
  122. Adams A et al. JHEP (10) 014 (2006)
  123. Hashimoto A, Itzhaki N Phys. Rev. D 63 126004 (2001)
  124. Lemaître G Ann. Soc. Sci. Bruxelles A 53 51 (1933)
  125. Tolman R C Proc. Natl. Acad. Sci. USA 20 169 (1934)
  126. Vaidya P C Proc. Indian Acad. Sci. A 33 264 (1951)
  127. Vaidya P C Nature 171 260 (1953); reprinted Gen. Relat. Grav. 31 119 (1999)
  128. Plebanski J, Stachel J J. Math. Phys. 9 269 (1968)
  129. Bonnor W B, Vaidya P C Gen. Relat. Grav. 1 127 (1970)
  130. Wang A, Wu Y Gen. Relat. Grav. 31 107 (1999)
  131. York J W (Jr.) Phys. Rev. D 31 775 (1985)
  132. Babichev E, Dokuchaev V, Eroshenko Yu Class. Quantum Grav. 29 115002 (2012)
  133. Dokuchaev V I, Eroshenko Yu N Phys. Rev. D 84 124022 (2011)
  134. Israel W Nuovo Cimento B 44 1 (1966)
  135. Israel W Nuovo Cimento B 48 463 (1967)
  136. Berezin V A, Kuzmin V A, Tkachev I I Phys. Rev. D 36 2919 (1987)
  137. Zel’dovich Ya B, Novikov I D Teoriya Tyagoteniya i Evolyutsiya Zvezd (M.: Nauka, 1971)
  138. Bogovalov S V Astron. Astrophys. 323 634 (1997)
  139. Whittaker J M Proc. R. Soc. Lond. A 306 1 (1968)
  140. Babichev E, Dokuchaev V, Eroshenko Yu Class. Quantum Grav. 22 143 (2005)
  141. Carter B Phys. Rev. 174 1559 (1968)
  142. López C A Gen. Relat. Grav. 29 1095 (1997)
  143. Christodoulou D Phys. Rev. Lett. 25 1596 (1970)
  144. Hawking S W Phys. Rev. Lett. 26 1344 (1971)
  145. González-Díaz P F Phys. Lett. B 586 1 (2004)
  146. Dokuchaev V I, Eroshenko Yu N arXiv:1012.4614
  147. Sawicki I, Vikman A Phys. Rev. D 87 067301 (2013)
  148. Landau L D, Lifshits E M Teoriya Polya (M.: Fizmatlit, 2012); Landau L D, Lifshitz E M The Classical Theory Of Fields (Oxford: Pergamon Press, 1975)
  149. Ivanov P Phys. Lett. B 680 212 (2009)
  150. Silva R, Lima J A S, Calvão M O Gen. Relat. Grav. 34 865 (2002)
  151. González-Díaz P F, Sigüenza C L Nucl. Phys. B 697 363 (2004)
  152. Braun S et al. Science 339 52 (2013)
  153. Cerf N J, Adami C Phys. Rev. Lett. 79 5194 (1997)
  154. Lima J A S, Alcaniz J S Phys. Lett. B 600 191 (2004)
  155. Silva R et al. Astron. Astrophys. 537 A11 (2012)
  156. Izquierdo G, Pavón D Phys. Lett. B 633 420 (2006)
  157. Pereira S H, Lima J A S Phys. Lett. B 669 266 (2008)
  158. Lima J A S, Pereira S H Phys. Rev. D 78 083504 (2008)
  159. Brevik I et al. Phys. Rev. D 70 043520 (2004)
  160. McInnes B JHEP (08) 029 (2002)
  161. Bouhmadi-López M, Madrid J A J JCAP (05) 005 (2005)
  162. Gurzadyan V G, Penrose R arXiv:1011.3706
  163. Carr B J, Coley A A Int. J. Mod. Phys. D 20 2733 (2011)
  164. Lukash V N Zh. Eksp. Teor. Fiz. 79 1601 (1980); Lukash V N Sov. Phys. JETP 52 807 (1980)
  165. Babichev E, Mukhanov V, Vikman A JHEP (09) 061 (2006)
  166. Bruneton J-P Phys. Rev. D 75 085013 (2007)
  167. Bruneton J-P, Esposito-Farèse G Phys. Rev. D 76 124012 (2007)
  168. Blokhintsev D I Prostranstvo i Vremya v Mikromire (M.: Nauka, 1982); Perevod 1-go izd., Blokhintsev D I Space And Time In The Microworld (Dordrecht: Reidel, 1973)
  169. Hashimoto A, Itzhaki N Phys. Rev. D 63 126004 (2001)
  170. Jacobson T, Mattingly D Phys. Rev. D 70 024003 (2004)
  171. Drummond I T, Hathrell S J Phys. Rev. D 22 343 (1980)
  172. Ohkuwa Y Prog. Theor. Phys. 65 1058 (1981)
  173. Scharnhorst K Phys. Lett. B 236 354 (1990)
  174. Dolgov A D, Khriplovich I B Zh. Eksp. Teor. Fiz. 85 1153 (1983); Dolgov A D, Khriplovich I B JETP 58 671 (1983)
  175. Dolgov A D, Novikov I D Phys. Lett. B 442 82 (1998)
  176. Liberati S, Sonego S, Visser M Ann. Physics 298 167 (2002)
  177. Hawking S W Phys. Rev. D 46 603 (1992)
  178. Gödel K Rev. Mod. Phys. 21 447 (1949)
  179. Gott J R (III) Phys. Rev. Lett. 66 1126 (1991)
  180. Ori A Phys. Rev. D 76 044002 (2007)
  181. Ori A Phys. Rev. Lett. 71 2517 (1993)
  182. Soen Y, Ori A Phys. Rev. D 54 4858 (1996)
  183. Ori A Phys. Rev. Lett. 95 021101 (2005)
  184. Mallett R L Found. Phys. 33 1307 (2003)
  185. Bonnor W B, Steadman B R Gen. Relat. Grav. 37 1833 (2005)
  186. Grøn Ø, Johannesen S New J. Phys. 10 103025 (2008)
  187. Morris M S, Thorne K S, Yurtsever U Phys. Rev. Lett. 61 1446 (1988)
  188. Aharonov Y, Komar A, Susskind L Phys. Rev. 182 1400 (1969)
  189. Gibbons G W, Herdeiro C A R Phys. Rev. D 63 064006 (2001)
  190. Gibbons G, Hashimoto K, PiljY JHEP (09) 061 (2002)
  191. Gibbons G W Class. Quantum Grav. 321 (2003)
  192. Gibbons G W Rev. Mex. Fis. 49 (S1) 19 (2003)
  193. Tolman R C The Theory Of The Relativity Of Motion (Berkeley: Univ. of California Press, 1917)
  194. Bonvin C, Caprini C, Durrer R arXiv:0706.1538
  195. Blas D, Deffayet C, Garriga J Class. Quantum Grav. 23 1697 (2006)
  196. Dubovsky S L, Sibiryakov S M Phys. Lett. B 638 509 (2006)
  197. Horndeski G W Int. J. Theor. Phys. 10 363 (1974)
  198. Fairlie D B, Govaerts J, Morozov A Nucl. Phys. B 373 214 (1992)
  199. Deffayet C, Deser S, Esposito-Farèse G Phys. Rev. D 82 061501(R) (2010)
  200. Dvali G, Gabadadze G, Porrati M Phys. Lett. B 485 208 (2000)
  201. Doroshkevich A et al. Phys. Rev. D 81 124011 (2010)
  202. Penrose R Riv. Nuovo Cimento (Numero Speziale I) 252 (1969)
  203. Penrose R Phys. Rev. Lett. 14 57 (1965)
  204. Penrose R "Structure of space-time" Battelle Rencontres, 1967, Seattle, Wash. (Lectures in Mathematics and Physics, Eds C M DeWitt, J A Wheeler) (New York: W.A. Benjamin, 1968) p. 121; Penrouz R Struktura Prostranstva-vremeni (M.: Mir, 1972)
  205. Penrose R Ann. NY Acad. Sci. 224 125 (1973)
  206. Penrose R Sci. Am. 226 (5) 38 (1972); Penrouz R Usp. Fiz. Nauk 109 355 (1973)
  207. Wald R Ann. Physics 82 548 (1974)
  208. Israel W Found. Phys. 14 1049 (1984)
  209. Bardeen J M Nature 226 64 (1970)
  210. Wald R M American Physical Society, APS/AAPT Joint Meeting, April 18 - 21, 1997, abstract #B4.01; Wald R M gr-qc/9710068
  211. Barausse E, Cardoso V, Khanna G Phys. Rev. Lett. 105 261102 (2010)
  212. Isoyama S, Sago N, Tanaka T Phys. Rev. D 84 124024 (2011)
  213. Bardeen J M Nature 226 64 (1970)
  214. Roman T A Gen. Relat. Grav. 20 359 (1988)
  215. Hod S Phys. Rev. Lett. 100 121101 (2008)
  216. Bondi H Proc. R. Soc. Lond. A 281 39 (1964)
  217. Bondi H, van der Burg M G J, Metzner A W K Proc. R. Soc. Lond. A 269 21 (1962)
  218. Nielsen A B Class. Quantum Grav. 27 245016 (2010)
  219. Bardeen J M, Carter B, Hawking S W Commun. Math. Phys. 31 161 (1973)
  220. Berezin V et al. Class. Quantum Grav. 22 4443 (2005)
  221. Visser M, Kar S, Dadhich N Phys. Rev. Lett. 90 201102 (2003)
  222. González-Díaz P F Phys. Rev. D 68 084016 (2003)

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