Geodesics and geodesic deviation in a two-dimensional black hole

American Journal of Physics

Volumn 71, Issue 10, 2003, Pages 1037-1042

  Koley, Ratna ^a   Pal, Supratik ^a   Kar, Sayan ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0141859838     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1566426     Document Type: Article

References (15)

1. A few of the standard texts on general relativity include R. D'Inverno, Introducing Einstein's Relativity (Oxford U.P., Oxford, 1995); B. Schutz, A First Course in General Relativity (Cambridge U.P., Cambridge, 1990); W. Rindler, Relativity (Oxford U.P., Oxford, 2001); S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1971); C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1972); L. Landau and E. M. Lifshitz, Classical Theory of Fields (Pergamon, Oxford, 1962); R. M. Wald, General Relativity (University of Chicago, Chicago, 1985).
2. A few of the standard texts on general relativity include R. D'Inverno, Introducing Einstein's Relativity (Oxford U.P., Oxford, 1995); B. Schutz, A First Course in General Relativity (Cambridge U.P., Cambridge, 1990); W. Rindler, Relativity (Oxford U.P., Oxford, 2001); S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1971); C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1972); L. Landau and E. M. Lifshitz, Classical Theory of Fields (Pergamon, Oxford, 1962); R. M. Wald, General Relativity (University of Chicago, Chicago, 1985).
3. A few of the standard texts on general relativity include R. D'Inverno, Introducing Einstein's Relativity (Oxford U.P., Oxford, 1995); B. Schutz, A First Course in General Relativity (Cambridge U.P., Cambridge, 1990); W. Rindler, Relativity (Oxford U.P., Oxford, 2001); S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1971); C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1972); L. Landau and E. M. Lifshitz, Classical Theory of Fields (Pergamon, Oxford, 1962); R. M. Wald, General Relativity (University of Chicago, Chicago, 1985).
4. A few of the standard texts on general relativity include R. D'Inverno, Introducing Einstein's Relativity (Oxford U.P., Oxford, 1995); B. Schutz, A First Course in General Relativity (Cambridge U.P., Cambridge, 1990); W. Rindler, Relativity (Oxford U.P., Oxford, 2001); S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1971); C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1972); L. Landau and E. M. Lifshitz, Classical Theory of Fields (Pergamon, Oxford, 1962); R. M. Wald, General Relativity (University of Chicago, Chicago, 1985).
5. A few of the standard texts on general relativity include R. D'Inverno, Introducing Einstein's Relativity (Oxford U.P., Oxford, 1995); B. Schutz, A First Course in General Relativity (Cambridge U.P., Cambridge, 1990); W. Rindler, Relativity (Oxford U.P., Oxford, 2001); S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1971); C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1972); L. Landau and E. M. Lifshitz, Classical Theory of Fields (Pergamon, Oxford, 1962); R. M. Wald, General Relativity (University of Chicago, Chicago, 1985).
6. A few of the standard texts on general relativity include R. D'Inverno, Introducing Einstein's Relativity (Oxford U.P., Oxford, 1995); B. Schutz, A First Course in General Relativity (Cambridge U.P., Cambridge, 1990); W. Rindler, Relativity (Oxford U.P., Oxford, 2001); S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1971); C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1972); L. Landau and E. M. Lifshitz, Classical Theory of Fields (Pergamon, Oxford, 1962); R. M. Wald, General Relativity (University of Chicago, Chicago, 1985).
7. A few of the standard texts on general relativity include R. D'Inverno, Introducing Einstein's Relativity (Oxford U.P., Oxford, 1995); B. Schutz, A First Course in General Relativity (Cambridge U.P., Cambridge, 1990); W. Rindler, Relativity (Oxford U.P., Oxford, 2001); S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1971); C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1972); L. Landau and E. M. Lifshitz, Classical Theory of Fields (Pergamon, Oxford, 1962); R. M. Wald, General Relativity (University of Chicago, Chicago, 1985).
8. For an extensive review of two-dimensional gravity, see D. Grumiller, W. Kummer, and D. Vassilevich, "Dilaton gravity in two dimensions," hep-th/0205253 (Phys. Rept. 369 (2002), 327-430) and references therein. A lucid introduction to string theory is available at 〈www.theory.caltech.edu/people/patricia (home page of Patricia Schwarz). More extensive texts on string theory are M. S. Green, J. H. Schwarz, and E. Witten, Superstring Theory (Cambridge U.P., Cambridge, 1987), Vols. I and II; J. Polchinski, String Theory (Cambridge U.P., Cambridge, 1998), Vols. I and II.
9. For an extensive review of two-dimensional gravity, see D. Grumiller, W. Kummer, and D. Vassilevich, "Dilaton gravity in two dimensions," hep-th/0205253 (Phys. Rept. 369 (2002), 327-430) and references therein. A lucid introduction to string theory is available at 〈www.theory.caltech.edu/people/patricia (home page of Patricia Schwarz). More extensive texts on string theory are M. S. Green, J. H. Schwarz, and E. Witten, Superstring Theory (Cambridge U.P., Cambridge, 1987), Vols. I and II; J. Polchinski, String Theory (Cambridge U.P., Cambridge, 1998), Vols. I and II.
10. For an extensive review of two-dimensional gravity, see D. Grumiller, W. Kummer, and D. Vassilevich, "Dilaton gravity in two dimensions," hep-th/0205253 (Phys. Rept. 369 (2002), 327-430) and references therein. A lucid introduction to string theory is available at 〈www.theory.caltech.edu/people/patricia (home page of Patricia Schwarz). More extensive texts on string theory are M. S. Green, J. H. Schwarz, and E. Witten, Superstring Theory (Cambridge U.P., Cambridge, 1987), Vols. I and II; J. Polchinski, String Theory (Cambridge U.P., Cambridge, 1998), Vols. I and II.
11. The original papers where this line element was first proposed are G. Mandai, A. M. Sengupta, and S. R. Wadia, "Classical solutions of two dimensional string theory," Mod. Phys. Lett. A 6, 1685-1692 (1991); E. Witten, "On string theory and black holes," Phys. Rev. D 44, 314-324 (1991).
12. The original papers where this line element was first proposed are G. Mandai, A. M. Sengupta, and S. R. Wadia, "Classical solutions of two dimensional string theory," Mod. Phys. Lett. A 6, 1685-1692 (1991); E. Witten, "On string theory and black holes," Phys. Rev. D 44, 314-324 (1991).
13. J. Harvey and A. Strominger, "Quantum aspects of black holes in string theory and quantum gravity," in String Theory and Quantum Gravity '92, edited by J. Harvey et al. (World Scientific, Singapore, 1993).
14. A good introduction to geodesics and geodesic deviation in particular is available in the text by R. D'Inverno referred to in Ref. 1.
15. ν = -1 (timelike condition). Therefore convergence/focusing occurs within a finite λ only if R ≤ 0. For some details on this (particularly in two dimensions and in the context of stringy black holes), see S. Kar, "Stringy black holes and energy conditions, " Phys. Rev. D 55, 4872-4879 (1997).