Advertisement

General Relativity and Astrophysics

  • Jayant V. Narlikar

Abstract

In 1915 Einstein published the final version of his basic general theory of relativity. Although he was to further modify it in 1917 by adding the so-called ‘lambda term’ the framework of the theory for local applications remained the same. For our reference we will take the form of the 1915 field equations as
$$ {R_{ik}} - \frac{1}{2}{g_{ik}}R = - \frac{{8\pi G}}{{{c^4}}}{T_{ik}}, $$
(3.1)
while those with the lambda term are:
$$ {R_{ik}} - \frac{1}{2}{g_{ik}}R + \lambda {g_{ik}} = - \frac{{8\pi G}}{{{c^4}}}{T_{ik}}, $$
(3.2)
Here the spacetime coordinates are x k , k = 0, 1, 2, 3, with 0 usually standing for the timelike dimension. The spacetime metric is g ik . The signature of the metric is [+,−,−,−]. T ik denotes the energy momentum tensor of the physical entities present in spacetime.

Keywords

Black Hole Gravitational Collapse Naked Singularity Gravitational Lens Raychaudhuri Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abramowicz MA and Prasanna AR MNRAS, 245: 720 (1990)ADSGoogle Scholar
  2. 2.
    Aquirregabiria JM and Vishveshwara CV. Phys. Lett. A, 210, 251 (1996)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Arun KG. Blanchet, Luc, Iyer, Bala R and Qusailah, Moh’d SS. Phys. Rev. D, 77, 064035 (2008)ADSCrossRefGoogle Scholar
  4. 4.
    Arun KG, Iyer, Bala R, Sathyaprakash BS, Sinha, Siddhartha and Broeck, Chris Van den: Phys. Rev. D., 76, 104016 (2007)Google Scholar
  5. 5.
    Arun K, Iyer BR, Qusailah MSS and Sathyaprakash BS. Class. Quant. Grav., 23, L37 (2006)ADSMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Bagchi M. et al. MNRAS, 387, 115 (2008)ADSCrossRefGoogle Scholar
  7. 7.
    Banerji A. Phys. Rev., 150,1086 (1966)ADSCrossRefGoogle Scholar
  8. 8.
    Banerji A and Duttachoudhury SB. GRG, 21,785 (1989)CrossRefGoogle Scholar
  9. 9.
    Banerji A. and Chakraborty D.S. IJMP, 12,1255 (2003)ADSCrossRefGoogle Scholar
  10. 10.
    Banerji A. Chatterjee S, and Dadhich NK. MPL, A17, 2335 (2003)ADSGoogle Scholar
  11. 11.
    Barnothy JM. A.J., 70, 666 (1965)ADSCrossRefGoogle Scholar
  12. 12.
    Blanchet Luc, Iyer, BR and Joguet B. Phys. Rev D., 65, 064005 (2002)ADSCrossRefGoogle Scholar
  13. 13.
    Blanchet L and Iyer BR., Phys. Rev. D, 71, 024004 (2005)ADSCrossRefGoogle Scholar
  14. 14.
    Blanchet L, Damour T. Esposito-Farèse, G. and Iyer, B.R. Phys. Rev. Lett., 93, 091101 (2004)ADSCrossRefGoogle Scholar
  15. 15.
    Blanchet, Luc, Faye, Guillaume, Iyer, Bala R, and Sinha Siddhartha, Class. Quant. Grav., 25, 165003 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    Blandford R and Narayan R., Astrophysical Journal, 310, 568–582 (1986)ADSCrossRefGoogle Scholar
  17. 17.
    Carlip, S. Class.Quant. Grav. 17, 4175 (2000)ADSMATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    Capovilla, and Guven, (1995)Google Scholar
  19. 19.
    Chitre SM and Narlikar JV. MNRAS, 187, 655 (1978)ADSCrossRefGoogle Scholar
  20. 20.
    Damour T, Gopakumar A and Iyer BR. Phys. Rev., D, 70, 064028 (2004)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    Damour T, Iyer BR, and Sathyaprakash BS. Phys. Rev. D., 57, 885 (1998)ADSCrossRefGoogle Scholar
  22. 22.
    Damour T, Iyer BR, and Sathyaprakash BS. Phys. Rev D., 63, 044023 (2001)ADSCrossRefGoogle Scholar
  23. 23.
    Datt B. Z. Phys., 108, 314 (1938)ADSCrossRefGoogle Scholar
  24. 24.
    Dadhich NK. Phys. Reps (1989)Google Scholar
  25. 25.
    Dey TK and Banerji S. Phys. Rev., D44, 325 (1991)ADSGoogle Scholar
  26. 26.
    Dey TK and Banerji S. Phys. Rev., D48, 3478 (1993)ADSGoogle Scholar
  27. 27.
    Dhurandhar SV and Sathyaprakash BS. Phys. Rev. D, 49, 1707 (1994)ADSCrossRefGoogle Scholar
  28. 28.
    Dhurandhar SV, Nayak R, and Vinet JY Phys. Rev. D., 65, 102002 (2002)ADSCrossRefGoogle Scholar
  29. 29.
    Dhurandhar SV, Vinet J-Y, and Nayak, KR. Class. and Quantum Grav., 25, 245002 (2008)ADSCrossRefGoogle Scholar
  30. 30.
    Eardley DM. Phys. Rev. Letts, 33, 442 (1974)ADSCrossRefGoogle Scholar
  31. 31.
    Einstein A. Preuss. Akad. Wiss. Berlin, Sitzber., 778, 799, 844 (1915)Google Scholar
  32. 32.
    Einstein A. Preuss. Akad. Wiss. Berlin, Sitzber., 142 (1917)Google Scholar
  33. 33.
    Einstein A, Infeld L. and Hoffmann B. Ann. Math., 39, 65 (1938)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    Friedmann A. Z. Phys., 10, 377, (1924) Z. Phys, 21, 326 (1922)ADSCrossRefGoogle Scholar
  35. 35.
    Geheniau J, and Debever R. Bull. Acad. Belg., 42, 114 (1956)MATHMathSciNetGoogle Scholar
  36. 36.
    Hawking SW, and Ellis GFR. The Large Scale Structure of Spacetime, Cambridge (1973)Google Scholar
  37. 37.
    Hoyle F, and Narlikar JV. Proc. R. Soc., A, (1962)Google Scholar
  38. 38.
    Joshi PS. Gravitational Collapse and Spacetime Singularities, (Cambridge University Press, Cambridge) (2007)MATHCrossRefGoogle Scholar
  39. 39.
    Joshi PS, and Dwivwdi IH. Phys. Rev., D47, 5357 (1993)ADSGoogle Scholar
  40. 40.
    Kar S. Phys. Rev., D52, 2036 (1995)ADSGoogle Scholar
  41. 41.
    Kar S. Phys. Rev., D53, 2071 (1996a)ADSMathSciNetGoogle Scholar
  42. 42.
    Kar S. Phys. Rev., D54, 6408 (1996b)ADSMathSciNetGoogle Scholar
  43. 43.
    Kar S. Phys. Rev., D55, 7921 (1997)ADSMathSciNetGoogle Scholar
  44. 44.
    Kaul RK. Phys. Rev., D68, 024026 (2003)ADSMathSciNetGoogle Scholar
  45. 45.
    Kaul RK, and P Majumdar. gr-qc/0002040, Phys. Rev. Letts., 84, 5255–5257 (2000)ADSCrossRefGoogle Scholar
  46. 46.
    Krishna Gopal, and Subramanian K. Nature, 349, 766–768 (1991)ADSCrossRefGoogle Scholar
  47. 47.
    Lemaitre, Abbé G. Annales de la Soc. Sci.de Bruxelles, XLVII A, 49 (1927)ADSGoogle Scholar
  48. 48.
    Lynds R, and Petrosian V. BAAS, 18, 1014 (1986)ADSGoogle Scholar
  49. 49.
    Lynds R, and Petrosian V. Astrophys. J., 336, 1–8 (1989)ADSCrossRefGoogle Scholar
  50. 50.
    Mitra S, Dhurandhar S, Souradeep T, Lazzarini A, Mandic V, Bose S, and Ballmer S. Phys. Rev. D., 77, 042002 (2008)ADSCrossRefGoogle Scholar
  51. 51.
    Nair S, Narasimha D, and Rao, AP. Astrophys. J., 407, 46–59 (1993)ADSCrossRefGoogle Scholar
  52. 52.
    Nair S, Garrett M. Mon. Not. R. Astr. Soc., 284, 58–72 (1997)ADSCrossRefGoogle Scholar
  53. 53.
    Nair S. MNRAS, 301, 315–322 (1998)ADSCrossRefGoogle Scholar
  54. 54.
    Narasimha D, and Chitre SM. Astrophys. J., 332, 75 (1988)ADSCrossRefGoogle Scholar
  55. 55.
    Narasimha D. and Chitre SM. Astron. and Astrophys., 280, 57–62 (1993)ADSGoogle Scholar
  56. 56.
    Narasimha D, Subramanian K, and Chitre SM., MNRAS, 200, 941–950 (1982)ADSCrossRefGoogle Scholar
  57. 57.
    Narasimha D, Subramanian K and Chitre SM. MNRAS, 210, 79–88 (1948a)ADSCrossRefGoogle Scholar
  58. 58.
    Narasimha D, Subramanian K, and SM Chitre. Astrophys. J., 283, 512–514 (1948b)ADSCrossRefGoogle Scholar
  59. 59.
    Narasimha D, Subramanian K, and Chitre SM. Nature, 321, 45–46 (1986)ADSCrossRefGoogle Scholar
  60. 60.
    Narlikar JV, Apparao MVK, and Dadhich NK. Nature, 251, 590 (1974)ADSCrossRefGoogle Scholar
  61. 61.
    Narlikar JV, Apparao MK. Ap.SS, 35, 321 (1975)CrossRefGoogle Scholar
  62. 62.
    Narlikar VV. Bombay Univ. J., 8, 31 (1939)MathSciNetGoogle Scholar
  63. 63.
    Narlikar VV, and Karmarkar KR. Proc. Ind. Acad. Sci., 29, 91 (1949)MATHMathSciNetGoogle Scholar
  64. 64.
    Narlikar VV and Rao BR. Proc. Nat. Inst. Sci, A21, 416 (1955)MathSciNetGoogle Scholar
  65. 65.
    Narlikar VV and singh KP. Proc. Nat. Inst. Sci., 17, 311 (1951)Google Scholar
  66. 66.
    Narlikar VV and Tiwari Ramji. Phys. Rev. Ser.2, 76, 868 (1949)MATHMathSciNetGoogle Scholar
  67. 67.
    Nayak KR, MacCallum MAH and Vishveshwara CV. Phys. Rev. D., 63, 024020 (2000)ADSMathSciNetCrossRefGoogle Scholar
  68. 68.
    Nityananda R. in: Gravitational lensing, Berlin and New York, Springer-Verlag, 3–12 (1990a)Google Scholar
  69. 69.
    Nityananda R. Current Science, 59, 1044 (1990b)Google Scholar
  70. 70.
    Nityananda R and Ostriker JP. Jour. Astrophys. and Astron., 5, 235–250 (1984)ADSCrossRefGoogle Scholar
  71. 71.
    Oppenheimer JR and Snyder H. Phys. Rev., 56, 455 (1939)ADSMATHCrossRefGoogle Scholar
  72. 72.
    Padmanabhan T and Subramanian K. MNRAS, 233, 265–284 (1988)ADSCrossRefGoogle Scholar
  73. 73.
    Padmanabhan T (2008) Gen. Rel. Grav. 40, 2031 (2008)ADSMATHMathSciNetCrossRefGoogle Scholar
  74. 74.
    Pai A, Dhurandhar SV, and Bose S. Phys. Rev. D., 64, 042004 (2001)ADSCrossRefGoogle Scholar
  75. 75.
    Ramachandra BS, and Vishveshwara CV. Class. Quant. Grav., 19, 127 (2002)ADSMATHMathSciNetCrossRefGoogle Scholar
  76. 76.
    Ramachandra BS, and Vishveshwara CV. Class. Quant. Grav., 20, 5253 (2003)ADSMATHMathSciNetCrossRefGoogle Scholar
  77. 77.
    Ramachandra BS, Nayak KR and Vishveshwara CV. Gen. Rel. and Grav., 37, 1977 (2003)ADSMathSciNetCrossRefGoogle Scholar
  78. 78.
    Raychaudhuri AK. Phys. Rev., 98, 1123 (1955)ADSMATHMathSciNetCrossRefGoogle Scholar
  79. 79.
    Refsdal S. MNRAS, 128, 295 (1964)ADSMATHMathSciNetCrossRefGoogle Scholar
  80. 80.
    Sahni V and Shtanov Y. JCAP, 11, 14 (2002)ADSMathSciNetGoogle Scholar
  81. 81.
    Sami M and Toporensky A. Mod. Phys. Lett., A19, 1509 (2004)ADSCrossRefGoogle Scholar
  82. 82.
    Sathyaprakash BS and Dhurandhar SV. Phys. Rev. D, 44, 3819 (1991)ADSCrossRefGoogle Scholar
  83. 83.
    Sen NR. Annls Phys., 4, 73 (1924)Google Scholar
  84. 84.
    Sen NR. Z. Phys., 40, 667 (1927)ADSCrossRefGoogle Scholar
  85. 85.
    Sen NR. Z. Astrophys., 7, 188 (1933)ADSGoogle Scholar
  86. 86.
    Sen NR. Z. Astrophys., 9, 215 (1934)ADSMATHGoogle Scholar
  87. 87.
    Sen NR. Z. Astrophys., 9, 315 (1935a)ADSMATHGoogle Scholar
  88. 88.
    Sen NR. Z. Astrophys., 10, 29 (1935b)Google Scholar
  89. 89.
    Sen NR. Z. Astrophys., 14, 157 (1937)ADSMATHGoogle Scholar
  90. 90.
    Sen NR. Ind. J. Phys., 15, 209 (1941)Google Scholar
  91. 91.
    Sen NR. and von Laue, M. Annls Phys., 4, 1882 (1924)Google Scholar
  92. 92.
    Sen NR and Roy TC. Z. Astrophys., 34, 84 (1924)ADSMathSciNetGoogle Scholar
  93. 93.
    Shtanov Y and Sahni V. Clss.Q. Grav., 19, L101 (2002)ADSMathSciNetCrossRefGoogle Scholar
  94. 94.
    Subramanian K, Chitre SM and Narasimha D. (1985), Astrophys. J., 289, 37–51 (1985)ADSCrossRefGoogle Scholar
  95. 95.
    Subramanian K. and Cowling SA. MNRAS, 219, 333–346 (1986)ADSCrossRefGoogle Scholar
  96. 96.
    Subrahmanyan R. and Rao AP. MNRAS, 231, 229 (1988)ADSCrossRefGoogle Scholar
  97. 97.
    Subrahmanyan K, Narasimha D, Rao AP and Swarup G. MNRAS, 246, 263 (1990)ADSGoogle Scholar
  98. 98.
    Vaidya PC. Curr. Sci., 12, 183 (1943)ADSMathSciNetGoogle Scholar
  99. 99.
    Vaidya PC. (1950)Google Scholar
  100. 100.
    Walsh D, Carswell RF and Weymann R J. Nature, 279, 381–384 (1979)ADSCrossRefGoogle Scholar
  101. 101.
    Zwicky F. Phys. Rev., 51, 679 (1937)ADSCrossRefGoogle Scholar

Copyright information

© Indian National Science Academy, New Delhi 2014

Authors and Affiliations

  1. 1.Inter-University Centre for Astronomy and AstrophysicsGaneshkhind, PuneIndia

Personalised recommendations