Relativistic images of Schwarzschild black hole lensing

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 79, Issue 8, 2009, Pages

  Virbhadra, K S ^a  

^a UNIVERSITY OF THE SCIENCES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 65849359184     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.79.083004     Document Type: Article

References (86)

1. A. Eddington, Space, Time and Gravitation (Cambridge Univ. Press, Cambridge, 1920).
2. P. Schneider, J. Ehlers, and E.E. Falco, Gravitational Lenses (Springer-Verlag, Berlin, 1992).
3. P. Schneider, C. Kochanek, and J. Wambsganss, Gravitational Lensing: Strong, Weak and Micro (Springer-Verlag, Berlin, 2006).
4. R. Narayan and M. Bartelmann, arXiv:astro-ph/9606001;
5. O. Wucknitz, arXiv:0709.4005.
6. C. Darwin, Proc. R. Soc. A PRLAAZ 0080-4630 249, 180 (1959); 10.1098/rspa.1959.0015
7. C. Darwin Proc. R. Soc. A PRLAAZ 0080-4630 263, 39 (1961). 10.1098/rspa.1961.0142
8. R. Atkinson, Astron. J. ANJOAA 0004-6256 70, 517 (1965). 10.1086/109775
9. S. Frittelli and E.T. Newman, Phys. Rev. D PRVDAQ 0556-2821 59, 124001 (1999). 10.1103/PhysRevD.59.124001
10. K.S. Virbhadra and G.F.R. Ellis, Phys. Rev. D PRVDAQ 0556-2821 62, 084003 (2000). 10.1103/PhysRevD.62.084003
11. S. Frittelli, T.P. Kling, and E.T. Newman, Phys. Rev. D PRVDAQ 0556-2821 61, 064021 (2000); 10.1103/PhysRevD.61.064021
12. T.P. Kling, E.T. Newman, and A. Perez, Phys. Rev. D PRVDAQ 0556-2821 62, 024025 (2000); 10.1103/PhysRevD.62.024025
13. T.P. Kling E.T. Newman A. Perez Phys. Rev. D PRVDAQ 0556-2821 62, 109901(E) (2000). 10.1103/PhysRevD.62.109901
14. V. Perlick, arXiv:0708.0178.
15. V. Perlick, Living Rev. Relativity 7, 9 (2004); 1433-8351
16. V. Perlick Phys. Rev. D PRVDAQ 0556-2821 69, 064017 (2004); 10.1103/PhysRevD.69.064017
17. V. Perlick Commun. Math. Phys. 220, 403 (2001); CMPHAY 0010-3616 10.1007/s002200100450
18. W. Hasse and V. Perlick, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 47, 042503 (2006); 10.1063/1.2188209
19. W. Hasse V. Perlick Gen. Relativ. Gravit. 34, 415 (2002); GRGVA8 0001-7701 10.1023/A:1015384604371
20. T. Foertsch, W. Hasse, and V. Perlick, Classical Quantum Gravity 20, 4635 (2003). CQGRDG 0264-9381 10.1088/0264-9381/20/21/006
21. P. Amore, M. Cervantes, A. De Pace, and F.M. Fernandez, Phys. Rev. D PRVDAQ 1550-7998 75, 083005 (2007); 10.1103/PhysRevD.75.083005
22. P. Amore and S. Arceo, Phys. Rev. D PRVDAQ 1550-7998 73, 083004 (2006); 10.1103/PhysRevD.73.083004
23. P. Amore, S. Arceo, and F.M. Fernandez, Phys. Rev. D PRVDAQ 1550-7998 74, 083004 (2006). 10.1103/PhysRevD.74.083004
24. A.F. Zakharov, F. De Paolis, G. Ingrosso, and A.A. Nucita, Astron. Astrophys. 442, 795 (2005); AAEJAF 0004-6361 10.1051/0004-6361:20053432
25. A.F. Zakharov, A.A. Nucita, F. De Paolis, and G. Ingrosso, New Astron. 10, 479 (2005); NAREF9 1387-6473 10.1016/j.newast.2005.02.007
26. A.F. Zakharov and Yu.V. Baryshev, Int. J. Mod. Phys. D 11, 1067 (2002); IMPDEO 0218-2718 10.1142/S0218271802002578
27. A.F. Zakharov Yu.V. Baryshev Classical Quantum Gravity 19, 1361 (2002). CQGRDG 0264-9381 10.1088/0264-9381/19/7/319
28. G.N. Gyulchev and S.S. Yazadjiev, Phys. Rev. D PRVDAQ 1550-7998 75, 023006 (2007); 10.1103/PhysRevD.75.023006
29. R. Whisker, Phys. Rev. D PRVDAQ 1550-7998 71, 064004 (2005); 10.1103/PhysRevD.71.064004
30. C.R. Keeton and A.O. Petters, Phys. Rev. D PRVDAQ 1550-7998 73, 044024 (2006); 10.1103/PhysRevD.73.044024
31. C.R. Keeton A.O. Petters Phys. Rev. D PRVDAQ 1550-7998 73, 104032 (2006); 10.1103/PhysRevD.73.104032
32. E.F. Eiroa, G.E. Romero, and D.F. Torres, Phys. Rev. D PRVDAQ 0556-2821 66, 024010 (2002); 10.1103/PhysRevD.66.024010
33. E.F. Eiroa, Phys. Rev. D PRVDAQ 1550-7998 73, 043002 (2006); 10.1103/PhysRevD.73.043002
34. A.O. Petters, Mon. Not. R. Astron. Soc. 338, 457 (2003); MNRAA4 0035-8711 10.1046/j.1365-8711.2003.06065.x
35. S.V. Iyer and A.O. Petters, Gen. Relativ. Gravit. 39, 1563 (2007); GRGVA8 0001-7701 10.1007/s10714-007-0481-8
36. N. Mukherjee and A.S. Majumdar, Gen. Relativ. Gravit. 39, 583 (2007); GRGVA8 0001-7701 10.1007/s10714-007-0407-5
37. A.S. Majumdar and N. Mukherjee, Mod. Phys. Lett. A 20, 2487 (2005); MPLAEQ 0217-7323 10.1142/S0217732305017676
38. E.F. Eiroa, Braz. J. Phys. 35, 1113 (2005); BJPHE6 0103-9733 10.1590/S0103-97332005000700026
39. E.F. Eiroa and G.E. Romero, Phys. Lett. B PYLBAJ 0370-2693 663, 377 (2008); 10.1016/j.physletb.2008.04.016
40. G.S. Bisnovatyi-Kogan and O.Yu. Tsupko, Astrophysics (Engl. Transl.) 51, 99 (2008). ATPYAA 0571-7256 10.1007/s10511-008-0011-8
41. S. Fernando and S. Roberts, Gen. Relativ. Gravit. 34, 1221 (2002); GRGVA8 0001-7701 10.1023/A:1019726501344
42. P. Mutka and P. Mahonen, Astrophys. J. 581, 1328 (2002); ASJOAB 0004-637X 10.1086/344438
43. C. Stornaiolo, Gen. Relativ. Gravit. 34, 2089 (2002); GRGVA8 0001-7701 10.1023/A:1021183417872
44. P. Mutka and P. Mahonen, Astrophys. J. 581, 1328 (2002); ASJOAB 0004-637X 10.1086/344438
45. K. Lake, Phys. Rev. D PRVDAQ 0556-2821 65, 087301 (2002); 10.1103/PhysRevD.65.087301
46. A. Bhadra, Phys. Rev. D PRVDAQ 0556-2821 67, 103009 (2003); 10.1103/PhysRevD.67.103009
47. R.A. Konoplya, Phys. Lett. B PYLBAJ 0370-2693 644, 219 (2007); 10.1016/j.physletb.2006.11.018
48. J. Briet and D. Hobill, arXiv:0801.3859.
49. V. Bozza, S. Capozziello, G. Iovane, and G. Scarpetta, Gen. Relativ. Gravit. 33, 1535 (2001). GRGVA8 0001-7701 10.1023/A:1012292927358
50. V. Bozza and L. Mancini, Gen. Relativ. Gravit. 36, 435 (2004). GRGVA8 0001-7701 10.1023/B:GERG.0000010486.58026.4f
51. K.S. Virbhadra, D. Narasimha, and S.M. Chitre, Astron. Astrophys. 337, 1 (1998). AAEJAF 0004-6361
52. K.S. Virbhadra and G.F.R. Ellis, Phys. Rev. D PRVDAQ 0556-2821 65, 103004 (2002). 10.1103/PhysRevD.65.103004
53. K.S. Virbhadra and C.R. Keeton, Phys. Rev. D PRVDAQ 1550-7998 77, 124014 (2008); 10.1103/PhysRevD.77.124014
54. See also K.S. Virbhadra C.R. Keeton arXiv:0710.2333V1 for more results in tables.
55. G.N. Gyulchev and S.S. Yazadjiev, Phys. Rev. D PRVDAQ 1550-7998 78, 083004 (2008); 10.1103/PhysRevD.78.083004
56. M.C. Werner and A.O. Petters, Phys. Rev. D PRVDAQ 1550-7998 76, 064024 (2007). 10.1103/PhysRevD.76.064024
57. M. Safonova and D.F. Torres, Mod. Phys. Lett. A 17, 1685 (2002); MPLAEQ 0217-7323 10.1142/S0217732302008083
58. J.M. Tejeiro and E.A. Larranaga, arXiv:gr-qc/0505054;
59. K.K. Nandi, Phys. Rev. D PRVDAQ 1550-7998 74, 024020 (2006); 10.1103/PhysRevD.74.024020
60. F. Rahaman, M. Kalam, and S. Chakraborty, Chin. J. Phys. (Taipei) CJOPAW 0577-9073 45, 518 (2007);
61. T.K. Dey and S. Sen, Mod. Phys. Lett. A 23, 953 (2008). MPLAEQ 0217-7323 10.1142/S0217732308025498
62. V. Kagramanova, J. Kunz, and C. Lämmerzahl, Phys. Lett. B PYLBAJ 0370-2693 634, 465 (2006); 10.1016/j.physletb.2006.01.069
63. I. Ciufolini and F. Ricci, Classical Quantum Gravity 19, 3863 (2002); CQGRDG 0264-9381 10.1088/0264-9381/19/15/301
64. I. Ciufolini F. Ricci Classical Quantum Gravity 19, 3875 (2002); CQGRDG 0264-9381 10.1088/0264-9381/19/15/302
65. S.S. Yazadjiev, arXiv:gr-qc/0305053;
66. M.P. Dabrowski and F.E. Schunck, Astrophys. J. 535, 316 (2000); ASJOAB 0004-637X 10.1086/308805
67. T. Matos and R. Becerril, Classical Quantum Gravity 18, 2015 (2001); CQGRDG 0264-9381 10.1088/0264-9381/18/11/303
68. V.A. De Lorenci, N. Figueiredo, H.H. Fliche, and M. Novello, Astron. Astrophys. 369, 690 (2001); AAEJAF 0004-6361 10.1051/0004-6361:20010089
69. F.E. Schunck, B. Fuchs, and E.W. Mielke, Mon. Not. R. Astron. Soc. 369, 485 (2006); MNRAA4 0035-8711 10.1111/j.1365-2966.2006.10330.x
70. K. Sarkar and A. Bhadra, Classical Quantum Gravity 23, 6101 (2006); CQGRDG 0264-9381 10.1088/0264-9381/23/22/002
71. Y. Chen, Z. Chen, and J. Wang, Gen. Relativ. Gravit. 39, 401 (2007); GRGVA8 0001-7701 10.1007/s10714-006-0393-z
72. B. Gwak, B-H. Lee, and W. Lee, arXiv:0806.4320.
73. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York, 1972).
74. F. Eisenhauer, Astrophys. J. 628, 246 (2005). ASJOAB 0004-637X 10.1086/430667
75. K. Gebhardt, http://hoku.as.utexas.edu/~gebhardt/blackhole.html.
76. V. Bozza and L. Mancini, Astrophys. J. 611, 1045 (2004). ASJOAB 0004-637X 10.1086/422309
77. E.F. Eiroa and D.F. Torres, Phys. Rev. D PRVDAQ 0556-2821 69, 063004 (2004). 10.1103/PhysRevD.69.063004
78. C.T. Cunningham and J.M. Bardeen, Astrophys. J. 183, 237 (1973). ASJOAB 0004-637X 10.1086/152223
79. K.P. Rauch and R.D. Blandford, Astrophys. J. 421, 46 (1994). ASJOAB 0004-637X 10.1086/173625
80. S.E. Vazquez and E.P. Esteban, Nuovo Cimento B NIFBAP 0369-4100 119, 489 (2004).
81. R. Penrose, in Black Holes and Relativistic Stars, edited by, R.M. Wald, (The University of Chicago, Chicago, 1998), p. 103;
82. K.S. Virbhadra, S. Jhingan, and P.S. Joshi, Int. J. Mod. Phys. D 6, 357 (1997); IMPDEO 0218-2718 10.1142/S0218271897000200
83. K.S. Virbhadra, Int. J. Mod. Phys. A 12, 4831 (1997); IMPAEF 0217-751X 10.1142/S0217751X97002577
84. K.S. Virbhadra Phys. Rev. D PRVDAQ 0556-2821 60, 104041 (1999). 10.1103/PhysRevD.60.104041
85. C-M. Claudel, K.S. Virbhadra, and G.F.R. Ellis, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 42, 818 (2001). 10.1063/1.1308507
86. K.S. Virbhadra, Gravitational lensing by Reissner-Nordström black holes and naked singularities (unpublished).