General Relativity and Gravitation

, Volume 42, Issue 9, pp 2269–2300

Gravitational lensing by black holes

Review Article

Abstract

We review the theoretical aspects of gravitational lensing by black holes, and discuss the perspectives for realistic observations. We will first treat lensing by spherically symmetric black holes, in which the formation of infinite sequences of higher order images emerges in the clearest way. We will then consider the effects of the spin of the black hole, with the formation of giant higher order caustics and multiple images. Finally, we will consider the perspectives for observations of black hole lensing, from the detection of secondary images of stellar sources and spots on the accretion disk to the interpretation of iron K-lines and direct imaging of the shadow of the black hole.

Keywords

Gravitational lensing Black holes Galactic center 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Darwin C.: Proc. R. Soc. Lond. A 249, 180 (1959)MATHMathSciNetADSGoogle Scholar
  2. 2.
    Weinberg S.: Gravitation and Cosmology. Wiley, New York (1972)Google Scholar
  3. 3.
    Claudel C.-M., Virbhadra K.S., Ellis G.F.R.: J. Math. Phys. 42, 818 (2001)MATHMathSciNetADSGoogle Scholar
  4. 4.
    Atkinson R.: Astron. J. 70, 517 (1965)ADSGoogle Scholar
  5. 5.
    Ohanian H.C.: Am. J. Phys. 55, 428 (1987)ADSGoogle Scholar
  6. 6.
    Virbhadra K.S., Ellis G.F.R.: Phys. Rev. D 62, 084003 (2000)MathSciNetADSGoogle Scholar
  7. 7.
    Bozza V., Capozziello S., Iovane G., Scarpetta G.: Gen. Relativ. Gravit. 33, 1535 (2001)MATHADSGoogle Scholar
  8. 8.
    Frittelli S., Newman E.T.: Phys. Rev. D 59, 124001 (1999)MathSciNetADSGoogle Scholar
  9. 9.
    Frittelli S., Kling T.P., Newman E.T.: Phys. Rev. D 61, 064021 (2000)MathSciNetADSGoogle Scholar
  10. 10.
    Perlick V.: Phys. Rev. D 69, 064017 (2004)MathSciNetADSGoogle Scholar
  11. 11.
    Perlick V.: Living Rev. Relativ. 7, 9 (2004)ADSGoogle Scholar
  12. 12.
    Nemiroff R.: Am. J. Phys. 61, 619 (1993)ADSGoogle Scholar
  13. 13.
    Bozza V.: Phys. Rev. D 78, 103005 (2008)MathSciNetADSGoogle Scholar
  14. 14.
    Luminet J.P.: A&A 75, 228 (1979)ADSGoogle Scholar
  15. 15.
    Holz D.E., Wheeler J.A.: ApJ 578, 330 (2002)ADSGoogle Scholar
  16. 16.
    Décanini Y., Folacci A.: Phys. Rev. D 81, 024031 (2010)ADSGoogle Scholar
  17. 17.
    Epstein R., Shapiro I.: Phys. Rev. D 22, 2947 (1980)ADSGoogle Scholar
  18. 18.
    Fischbach E., Freeman B.S.: Phys. Rev. D 22, 2950 (1980)ADSGoogle Scholar
  19. 19.
    Richter G., Matzner R.: Phys. Rev. D 26, 1219 (1982)ADSGoogle Scholar
  20. 20.
    Richter G., Matzner R.: Phys. Rev. D 26, 2549 (1982)ADSGoogle Scholar
  21. 21.
    Sarmiento A.F.: Gen. Relativ. Gravit. 14, 793 (1982)ADSGoogle Scholar
  22. 22.
    Sereno M.: Phys. Rev. D 67, 064007 (2003)MathSciNetADSGoogle Scholar
  23. 23.
    Keeton C.R., Petters A.O.: Phys. Rev. D 72, 104006 (2005)MathSciNetADSGoogle Scholar
  24. 24.
    Keeton C.R., Petters A.O.: Phys. Rev. D 73, 044024 (2006)MathSciNetADSGoogle Scholar
  25. 25.
    Keeton C.R., Petters A.O.: Phys. Rev. D 73, 104032 (2006)MathSciNetADSGoogle Scholar
  26. 26.
    Ebina J., Osuga T., Asada H., Kasai M.: Prog. Theor. Phys. 104, 1317 (2000)ADSGoogle Scholar
  27. 27.
    Lewis G.F., Wang X.R.: Prog. Theor. Phys. 105, 893 (2001)ADSGoogle Scholar
  28. 28.
    Sereno M.: Phys. Rev. D 69, 023002 (2004)ADSGoogle Scholar
  29. 29.
    Damour Th., Esposito-Farèse G.: Phys. Rev. D 53, 5541 (1996)MathSciNetADSGoogle Scholar
  30. 30.
    Sereno M.: Phys. Rev. D 77, 043004 (2008)MathSciNetADSGoogle Scholar
  31. 31.
    Chandrasekhar S.: Mathematical Theory of Black Holes. Clarendon Press, Oxford (1983)MATHGoogle Scholar
  32. 32.
    Eiroa E.F., Romero G.E., Torres D.F.: Phys. Rev. D 66, 024010 (2002)MathSciNetADSGoogle Scholar
  33. 33.
    Bozza V.: Phys. Rev. D 66, 103001 (2002)ADSGoogle Scholar
  34. 34.
    Eiroa E.F., Torres D.F.: Phys. Rev. D 69, 063004 (2004)ADSGoogle Scholar
  35. 35.
    Bozza V., Scarpetta G.: Phys. Rev. D 76, 083008 (2007)ADSGoogle Scholar
  36. 36.
    Bhadra A.: Phys. Rev. D 67, 103009 (2003)MathSciNetADSGoogle Scholar
  37. 37.
    Eiroa E.F.: Phys. Rev. D 71, 083010 (2005)ADSGoogle Scholar
  38. 38.
    Whisker R.: Phys. Rev. D 71, 064004 (2005)ADSGoogle Scholar
  39. 39.
    Majumdar A.S., Mukherjee N.: Int. J. Mod. Phys. D 14, 1095 (2005)MATHADSGoogle Scholar
  40. 40.
    Eiroa E.F.: Phys. Rev. D 73, 043002 (2006)MathSciNetADSGoogle Scholar
  41. 41.
    Nandi K.K., Zhang Y.-Z., Zakharov A.V.: Phys. Rev. D 74, 024020 (2006)ADSGoogle Scholar
  42. 42.
    Sarkar K., Bhadra A.: Class. Quant. Gravit. 23, 6101 (2006)MATHMathSciNetADSGoogle Scholar
  43. 43.
    Mukherjee N., Majumdar A.S.: Gen. Relat. Gravit. 39, 583 (2007)MATHMathSciNetADSGoogle Scholar
  44. 44.
    Rahaman F., Kalam M., Chakraborty S.: Chin. J. Phys. 45, 518 (2007)Google Scholar
  45. 45.
    Dey T.K., Sen S.: Mod. Phys. Lett. A 23, 953 (2008)MATHMathSciNetADSGoogle Scholar
  46. 46.
    Chen S., Jing J.: Phys. Rev. D 80, 024036 (2009)MathSciNetADSGoogle Scholar
  47. 47.
    Ghosh T., Sengupta S.: Phys. Rev. D 81, 044013 (2010)ADSGoogle Scholar
  48. 48.
    Bozza V.: Nuovo Cimento B 122, 547 (2007)MathSciNetADSGoogle Scholar
  49. 49.
    Iyer S.V., Petters A.O.: Gen. Relat. Gravit. 39, 1563 (2007)MATHMathSciNetADSGoogle Scholar
  50. 50.
    Bozza V., Mancini L.: Gen. Relat. Gravit. 36, 435 (2004)MATHMathSciNetADSGoogle Scholar
  51. 51.
    Chang K., Refsdal S.: Nature 282, 561 (1979)ADSGoogle Scholar
  52. 52.
    Chang K., Refsdal S.: A& A 132, 168 (1984)ADSGoogle Scholar
  53. 53.
    Poisson E.: Phys. Rev. Lett. 94, 161103 (2005)MathSciNetADSGoogle Scholar
  54. 54.
    Bozza V., Sereno M.: Phys. Rev. D 73, 103004 (2006)ADSGoogle Scholar
  55. 55.
    Konoplya R.A.: Phys. Lett. B 644, 219 (2007)MathSciNetADSGoogle Scholar
  56. 56.
    Amore P., Arceo S.: Phys. Rev. D 73, 083004 (2006)MathSciNetADSGoogle Scholar
  57. 57.
    Amore P., Arceo S., Fernandez F.M.: Phys. Rev. D 74, 083004 (2006)ADSGoogle Scholar
  58. 58.
    Amore P., Cervantes M., De Pace A., Fernandez F.M.: Phys. Rev. D 75, 083005 (2007)ADSGoogle Scholar
  59. 59.
    Carter B.: Phys. Rev. 174, 1559 (1968)MATHADSGoogle Scholar
  60. 60.
    Rauch K.P., Blandford R.D.: ApJ 421, 46 (1994)ADSGoogle Scholar
  61. 61.
    Karas V., Vokrouhlicky D., Polnarev A.G.: MNRAS 259, 569 (1992)ADSGoogle Scholar
  62. 62.
    Viergutz S.U.: A&A 272, 355 (1993)MathSciNetADSGoogle Scholar
  63. 63.
    Fanton C., Calvani M., de Felice F., Cadez A.: PASJ 49, 159 (1997)ADSGoogle Scholar
  64. 64.
    Dexter J., Agol E.: ApJ 696, 1616 (2009)ADSGoogle Scholar
  65. 65.
    Iyer S.V., Hansen E.C.: Phys. Rev. D 80, 124023 (2009)ADSGoogle Scholar
  66. 66.
    Hasse W., Perlick V.: J. Math. Phys. 47, 042503 (2006)MathSciNetADSGoogle Scholar
  67. 67.
    Pineault S., Roeder R.C.: ApJ 212, 541 (1977)MathSciNetADSGoogle Scholar
  68. 68.
    Pineault S., Roeder R.C.: ApJ 213, 548 (1977)ADSGoogle Scholar
  69. 69.
    Bray I.: Phys. Rev. D 34, 367 (1986)MathSciNetADSGoogle Scholar
  70. 70.
    Edery A., Godin J.: Gen. Relat. Gravit. 38, 1715 (2006)MATHMathSciNetADSGoogle Scholar
  71. 71.
    Werner M.C., Petters A.O.: Phys. Rev. D 76, 064024 (2007)ADSGoogle Scholar
  72. 72.
    Asada H., Kasai M.: Prog. Theor. Phys. 104, 95 (2000)ADSGoogle Scholar
  73. 73.
    Asada H., Kasai M., Yamamoto T.: Phys. Rev. D 67, 043006 (2003)ADSGoogle Scholar
  74. 74.
    Sereno M., De Luca F.: Phys. Rev. D 74, 123009 (2006)ADSGoogle Scholar
  75. 75.
    Sereno M., De Luca F.: Phys. Rev. D 78, 023008 (2008)MathSciNetADSGoogle Scholar
  76. 76.
    Vazquez S.E., Esteban E.P.: Nuovo Cimento B 119, 489 (2004)MathSciNetADSGoogle Scholar
  77. 77.
    Bozza V.: Phys. Rev. D 67, 103006 (2003)ADSGoogle Scholar
  78. 78.
    Bozza V., De Luca F., Scarpetta G., Sereno M.: Phys. Rev. D 72, 083003 (2005)MathSciNetADSGoogle Scholar
  79. 79.
    Bozza V., De Luca F., Scarpetta G.: Phys. Rev. D 74, 063001 (2006)ADSGoogle Scholar
  80. 80.
    Gyulchev G.N., Yazadjiev S.S.: Phys. Rev. D75, 023006 (2007)MathSciNetADSGoogle Scholar
  81. 81.
    Aliev A.N., Talazan P.: Phys. Rev. D80, 044023 (2009)MathSciNetADSGoogle Scholar
  82. 82.
    Gyulchev G.N., Yazadjiev S.S.: Phys. Rev. D 81, 023005 (2010)ADSGoogle Scholar
  83. 83.
    de Vries A.: Class. Quant. Gravit. 17, 123 (2000)MATHADSGoogle Scholar
  84. 84.
    Bambi C., Freese K.: Phys. Rev. D 79, 043002 (2009)MathSciNetADSGoogle Scholar
  85. 85.
    Bardeen J.: In: De Witt, C., De Witt, B.S. (eds) Black Holes. École d’été de Physique Théorique, Les Houches 1972, Gordon & Breach Science Publishers, New York (1973)Google Scholar
  86. 86.
    Takahashi R.: ApJ 611, 996 (2004)ADSGoogle Scholar
  87. 87.
    Takahashi R.: Publ. Astron. Soc. Jpn. 57, 273 (2005)ADSGoogle Scholar
  88. 88.
    Zakharov A.F. et al.: A& A 442, 795 (2005)ADSGoogle Scholar
  89. 89.
    Hioki K., Maeda K.-I.: Phys. Rev. D 80, 024042 (2009)ADSGoogle Scholar
  90. 90.
    Cunningham C.T., Bardeen J.M.: ApJ 173, L137 (1972)ADSGoogle Scholar
  91. 91.
    Cunningham C.T., Bardeen J.M.: ApJ 183, 237 (1973)ADSGoogle Scholar
  92. 92.
    Bozza V.: Phys. Rev. D 78, 063014 (2008)MathSciNetADSGoogle Scholar
  93. 93.
    Richstone D. et al.: Nature 395, A14 (1998)ADSGoogle Scholar
  94. 94.
    Gillessen S. et al.: ApJ 692, 1075 (2009)ADSGoogle Scholar
  95. 95.
    Macchetto F. et al.: ApJ 489, 579 (1997)ADSGoogle Scholar
  96. 96.
    Genzel R. et al.: Nature 425, 934 (2003)ADSGoogle Scholar
  97. 97.
    Melia F.: The Black Hole at the Center of Our Galaxy. Princeton University Press, Princeton (2003)Google Scholar
  98. 98.
    Wardle M., Yusuf-Zadeh F.: ApJ 387, L65 (1992)ADSGoogle Scholar
  99. 99.
    Jaroszyński M.: Acta Astron. 48, 413 (1998)ADSGoogle Scholar
  100. 100.
    Alexander T., Sternberg A.: ApJ 520, 137 (1999)ADSGoogle Scholar
  101. 101.
    Alexander T.: ApJ 553, L149 (2001)ADSGoogle Scholar
  102. 102.
    Chanamé J., Gould A., Miralda-Escudé J.: ApJ 563, 793 (2001)ADSGoogle Scholar
  103. 103.
    Alexander T., Loeb A.: ApJ 551, 223 (2001)ADSGoogle Scholar
  104. 104.
    Nusser A., Broadhurst T.: MNRAS 355, L6 (2004)ADSGoogle Scholar
  105. 105.
    Petters A.O.: MNRAS 338, 457 (2003)ADSGoogle Scholar
  106. 106.
    Abramovicz M.A., Lanza A., Spiegel E.A., Szuszkiewicz E.: Nature 356, 41 (1992)ADSGoogle Scholar
  107. 107.
    Karas V., Bao G.: A&A 257, 531 (1992)ADSGoogle Scholar
  108. 108.
    Bao G.: A&A 257, 594 (1992)ADSGoogle Scholar
  109. 109.
    Zakharov A.F.: MNRAS 269, 283 (1994)ADSGoogle Scholar
  110. 110.
    Bao G., Hadrava P., Østgaard E.: ApJ 425, 63 (1994)ADSGoogle Scholar
  111. 111.
    Bao G., Østgaard E.: ApJ 443, 54 (1995)ADSGoogle Scholar
  112. 112.
    Hollywood J.M. et al.: ApJ 448, L21 (1995)ADSGoogle Scholar
  113. 113.
    Karas V.: ApJ 470, 743 (1996)ADSGoogle Scholar
  114. 114.
    Karas V.: MNRAS 288, 12 (1997)ADSGoogle Scholar
  115. 115.
    Karas V.: PASJ 51, 317 (1999)ADSGoogle Scholar
  116. 116.
    Fukue J.: PASJ 55, 1121 (2003)ADSGoogle Scholar
  117. 117.
    Schödel R. et al.: ApJ 596, 1015 (2003)ADSGoogle Scholar
  118. 118.
    Ghez A.M. et al.: ApJ 620, 744 (2005)ADSGoogle Scholar
  119. 119.
    De Paolis F., Geralico A., Ingrosso G., Nucita A.A.: A&A 409, 809 (2003)MATHADSGoogle Scholar
  120. 120.
    Bozza V., Mancini L.: ApJ 611, 1045 (2004)ADSGoogle Scholar
  121. 121.
    Bozza V., Mancini L.: ApJ 627, 790 (2005)ADSGoogle Scholar
  122. 122.
    Bozza V., Mancini L.: ApJ 696, 701 (2009)ADSGoogle Scholar
  123. 123.
    Eisenhauer, et al.: Proc SPIE 7013, 70132 (2008)Google Scholar
  124. 124.
    Muno M.P. et al.: ApJ 622, L113 (2005)ADSGoogle Scholar
  125. 125.
    Tanaka Y. et al.: Nature 375, 659 (1995)ADSGoogle Scholar
  126. 126.
    Cunningham C.T.: ApJ 202, 788 (1975)ADSGoogle Scholar
  127. 127.
    Asaoka I.: PASJ 41, 763 (1989)ADSGoogle Scholar
  128. 128.
    Jaroszyński M., Kurpiewski A.: A&A 326, 419 (1997)ADSGoogle Scholar
  129. 129.
    Fabian A.C., Rees M.J., Stella L., White N.E.: MNRAS 238, 729 (1989)ADSGoogle Scholar
  130. 130.
    Stella L.: Nature 344, 747 (1990)ADSGoogle Scholar
  131. 131.
    Laor A.: ApJ 376, 90 (1991)ADSGoogle Scholar
  132. 132.
    Kojima Y.: MNRAS 250, 629 (1991)ADSGoogle Scholar
  133. 133.
    Chen K., Eardley D.: ApJ 382, 125 (1991)ADSGoogle Scholar
  134. 134.
    Bao G.: ApJ 409, L41 (1993)ADSGoogle Scholar
  135. 135.
    Matt G., Perola G.C., Stella L.: A&A 267, 643 (1993)ADSGoogle Scholar
  136. 136.
    Hameury J.-M., Marck J.-A., Pelat D.: A&A 287, 795 (1994)ADSGoogle Scholar
  137. 137.
    Bao G., Hadrava P., Østgaard E.: ApJ 435, 55 (1994)ADSGoogle Scholar
  138. 138.
    Bao G., Hadrava P., Østgaard E.: ApJ 464, 684 (1996)ADSGoogle Scholar
  139. 139.
    Bromley B.C., Chen K., Miller W.A.: ApJ 475, 57 (1997)ADSGoogle Scholar
  140. 140.
    Reynolds Ch.S., Young A.J., Begelman M.C., Fabian A.C.: ApJ 514, 164 (1999)ADSGoogle Scholar
  141. 141.
    Martocchia A., Karas V., Matt G.: MNRAS 312, 817 (2000)ADSGoogle Scholar
  142. 142.
    Yu Q., Lu Y.: MNRAS 311, 161 (2000)ADSGoogle Scholar
  143. 143.
    Dovciak M., Karas V., Yaqoob T.: ApJS 153, 205 (2004)ADSGoogle Scholar
  144. 144.
    Beckwith K., Done Ch.: MNRAS 352, 353 (2004)ADSGoogle Scholar
  145. 145.
    Fukumura K., Tsuruta S.: ApJ 613, 700 (2004)ADSGoogle Scholar
  146. 146.
    Czerny B. et al.: A&A 420, 1 (2004)ADSGoogle Scholar
  147. 147.
    Cadež A., Calvani M.: MNRAS 363, 177 (2005)ADSGoogle Scholar
  148. 148.
    Goosmann R.W.: A&A 454, 741 (2006)ADSGoogle Scholar
  149. 149.
    Zakharov A.F., Repin S.V.: New Astron. 11, 405 (2006)ADSGoogle Scholar
  150. 150.
    Fuerst S.V., Wu K.: A&A 474, 55 (2007)MATHADSGoogle Scholar
  151. 151.
    Repin S.V., Lukash V.N., Strokov V.N.: Astron. Rep. 52, 1 (2008)ADSGoogle Scholar
  152. 152.
    Fabian A.C. et al.: Nature 459, 540 (2009)ADSGoogle Scholar
  153. 153.
    Fukue J., Yokoyama T.: PASJ 40, 15 (1988)ADSGoogle Scholar
  154. 154.
    Falcke H., Melia F., Agol E.: ApJ 528, L13 (1999)ADSGoogle Scholar
  155. 155.
    Bromley B.C., Melia F., Liu S.: ApJ 555, L83 (2001)ADSGoogle Scholar
  156. 156.
    Fukue J.: PASJ 55, 155 (2003)ADSGoogle Scholar
  157. 157.
    Takahashi R.: ApJ 611, 996 (2004)ADSGoogle Scholar
  158. 158.
    Beckwith K., Done C.: MNRAS 359, 1217 (2005)ADSGoogle Scholar
  159. 159.
    Broderick A.E., Narayan R.: ApJ 638, L21 (2006)ADSGoogle Scholar
  160. 160.
    Yuan F., Shen Zh.-Q., Huang L.: ApJ 642, L45 (2006)ADSGoogle Scholar
  161. 161.
    Huang L., Cai M., Shen Zh.-Q., Yuan F.: MNRAS 379, 833 (2007)ADSGoogle Scholar
  162. 162.
    Yuan Y.-F., Cao Z., Huang L., Shen Zh.-Q.: ApJ 699, 722 (2009)ADSGoogle Scholar
  163. 163.
    Lo K.Y. et al.: ApJ 508, L61 (1998)ADSGoogle Scholar
  164. 164.
    Krichbaum, T.P., et al. In: Proc. 6th European VLBI Network Symposium, Bonn, Germany (2002)Google Scholar
  165. 165.
    Krichbaum T.P. et al.: J. Phys. Conf. Ser. 54, 328 (2006)ADSGoogle Scholar
  166. 166.
    Broderick A.E., Loeb A.: ApJ 697, 1164 (2009)ADSGoogle Scholar
  167. 167.
    Krichbaum, T.P., et al.: arXiv:0812.4211Google Scholar
  168. 168.
    Doeleman Sh.S. et al.: Nature 455, 78 (2008)ADSGoogle Scholar
  169. 169.
    Dexter J., Agol E., Fragile P.C.: APJ 703, L142 (2009)ADSGoogle Scholar
  170. 170.
    Broderick A.E., Loeb A.: MNRAS 363, 353 (2005)ADSGoogle Scholar
  171. 171.
    Broderick A.E., Loeb A.: MNRAS 367, 905 (2006)ADSGoogle Scholar
  172. 172.
    Broderick A.E., Loeb A.: ApJ 636, L109 (2006)ADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Dipartimento di Fisica, E. R. CaianielloUniversità di SalernoFiscianoItaly
  2. 2.Sezione di NapoliIstituto Nazionale di Fisica NucleareNaplesItaly
  3. 3.Istituto Internazionale per gli Alti Studi ScientificiVietri sul MareItaly

Personalised recommendations