Observables for two-dimensional black holes

J. Gegenberg; G. Kunstatter; D. Louis-Martinez

doi:10.1103/PhysRevD.51.1781

Access by Xinjiang University

Observables for two-dimensional black holes

J. Gegenberg

G. Kunstatter and D. Louis-Martinez

Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 5A3

Department of Physics and Winnipeg Institute of Theoretical Physics, University of Winnipeg, Winnipeg, Manitoba, Canada R3B 2E9

PDF

Phys. Rev. D 51, 1781 – Published 15 February, 1995

DOI: https://doi.org/10.1103/PhysRevD.51.1781

Abstract

We consider the most general dilaton gravity theory in 1+1 dimensions. By suitably parametrizing the metric and scalar field we find a simple expression that relates the energy of a generic solution to the magnitude of the corresponding Killing vector. In theories that admit black hole solutions, this relationship leads directly to an expression for the entropy S=2π $τ_{0}$ /G, where $τ_{0}$ is the value of the scalar field (in this parametrization) at the event horizon. This result agrees with the one obtained using the more general method of Wald. Finally, we point out an intriguing connection between the black hole entropy and the imaginary part of the ‘‘phase’’ of the exact Dirac quantum wave functionals for the theory.

References (17)

C. G. Callan, S. B. Giddings, J. A. Harvey and A. Strominger, Phys. Rev. D 45, R1005 (1992). See also S. Hawking, Phys. Rev. Lett. 69, 406 (1992). For reviews, see J. A. Harvey and A. Strominger, in Recent Directions in Particle Theory From Superstrings and Black Holes to the Standard Model, Proceedings of the Theoretical Advanced Study Institute, Boulder, Colorado, 1992, edited by J. Harvey and J. Polchinski (World Scientific, Singapore, 1993); S. B. Giddings, in String Quantum Gravity and Physics at the Planck Energy Scale, Proceedings of the International Workshop, Erice, Italy, 1992, edited by N. Sanchez (World Scientific, Singapore, 1993), p. 437.
T. Banks and M. O'Laughlin, Nucl. Phys. B362, 649 (1991).
See also R. B. Mann, Phys. Rev. D 47, 4438 (1993); J. P. S. Lemos and P. M. Sa, ibid. 49, 2897 (1994).
R. Jackiw, in Quantum Theory of Gravity, edited by S. Christensen (Hilger, Bristol, 1984), p. 403; C. Teitelboim, in ibid., p. 327; M. Henneaux, Phys. Rev. Lett. 54, 959 (1985).
B. K. Berger, D. M. Chitre, V. E. Moncrief and Y. Nutku, Phys. Rev. D 5, 2467 (1973); W. G. Unruh, ibid. 14, 870 (1976); G. A. Vilkovisky and V. F. Frolov, in Quantum Gravity, Proceedings of the 2nd Seminar, Moscow, USSR, 1981, edited by M. A. Markov and P. C. West (Plenum, London, 1983), p. 267; P. Thomi, B. Isaak and P. Hajicek, Phys. Rev. D 30, 1168 (1984); P. Hajicek, ibid. 30, 1178 (1984); T. Thiemann and H. A. Kastrup, Nucl. Phys. B399, 211 (1993); J. Gegenberg and G. Kunstatter, Phys. Lett. B 233, 331 (1989).
C. Teitelboim, Phys. Rev. D 28, 310 (1993); H. A. Kastrup and T. Thiemann, Nucl. Phys. B425, 665 (1994).
K. Kuchar, Phys. Rev. D 50, 3961 (1994).
D. Loius Martinez, J. Gegenberg and G. Kunstatter, Phys. Lett. B 321, 193 (1994).
D. Louis Martinez and G. Kunstatter, Phys. Rev. D 49, 5227 (1994).
C. G. Torre, Phys. Rev. D 40, 2588 (1989).
P. A. M. Dirac, Lectures on Quantum Mechanics, Belfar Graduate School of Science (Yeshiva University, New York, 1964).
See, for example, R. M. Wald, General Relativity (Chicago University Press, Chicago, 1984), p. 332.
R. M. Wald, Phys. Rev. D 48, R3427 (1993).
J. Lee and R. M. Wald, J. Math. Phys. 31, 2378 (1990).
V. P. Frolov, Phys. Rev. D 46, 5383 (1992).
V. Iyer and R. M. Wald, Phys. Rev. D 50, 846 (1994).
J. Gegenberg and G. Kunstatter, Phys. Rev. D 47, R4192 (1993).

[c1] C. G. Callan, S. B. Giddings, J. A. Harvey and A. Strominger, Phys. Rev. D 45, R1005 (1992). See also S. Hawking, Phys. Rev. Lett. 69, 406 (1992). For reviews, see J. A. Harvey and A. Strominger, in Recent Directions in Particle Theory From Superstrings and Black Holes to the Standard Model, Proceedings of the Theoretical Advanced Study Institute, Boulder, Colorado, 1992, edited by J. Harvey and J. Polchinski (World Scientific, Singapore, 1993); S. B. Giddings, in String Quantum Gravity and Physics at the Planck Energy Scale, Proceedings of the International Workshop, Erice, Italy, 1992, edited by N. Sanchez (World Scientific, Singapore, 1993), p. 437.

[c2] T. Banks and M. O'Laughlin, Nucl. Phys. B362, 649 (1991).

[c3] See also R. B. Mann, Phys. Rev. D 47, 4438 (1993); J. P. S. Lemos and P. M. Sa, ibid. 49, 2897 (1994).

[c4] R. Jackiw, in Quantum Theory of Gravity, edited by S. Christensen (Hilger, Bristol, 1984), p. 403; C. Teitelboim, in ibid., p. 327; M. Henneaux, Phys. Rev. Lett. 54, 959 (1985).

[c5] B. K. Berger, D. M. Chitre, V. E. Moncrief and Y. Nutku, Phys. Rev. D 5, 2467 (1973); W. G. Unruh, ibid. 14, 870 (1976); G. A. Vilkovisky and V. F. Frolov, in Quantum Gravity, Proceedings of the 2nd Seminar, Moscow, USSR, 1981, edited by M. A. Markov and P. C. West (Plenum, London, 1983), p. 267; P. Thomi, B. Isaak and P. Hajicek, Phys. Rev. D 30, 1168 (1984); P. Hajicek, ibid. 30, 1178 (1984); T. Thiemann and H. A. Kastrup, Nucl. Phys. B399, 211 (1993); J. Gegenberg and G. Kunstatter, Phys. Lett. B 233, 331 (1989).

[c6] C. Teitelboim, Phys. Rev. D 28, 310 (1993); H. A. Kastrup and T. Thiemann, Nucl. Phys. B425, 665 (1994).

[c7] K. Kuchar, Phys. Rev. D 50, 3961 (1994).

[c8] D. Loius Martinez, J. Gegenberg and G. Kunstatter, Phys. Lett. B 321, 193 (1994).

[c9] D. Louis Martinez and G. Kunstatter, Phys. Rev. D 49, 5227 (1994).

[c10] C. G. Torre, Phys. Rev. D 40, 2588 (1989).

[c11] P. A. M. Dirac, Lectures on Quantum Mechanics, Belfar Graduate School of Science (Yeshiva University, New York, 1964).

[c12] See, for example, R. M. Wald, General Relativity (Chicago University Press, Chicago, 1984), p. 332.

[c13] R. M. Wald, Phys. Rev. D 48, R3427 (1993).

[c14] J. Lee and R. M. Wald, J. Math. Phys. 31, 2378 (1990).

[c15] V. P. Frolov, Phys. Rev. D 46, 5383 (1992).

[c16] V. Iyer and R. M. Wald, Phys. Rev. D 50, 846 (1994).

[c17] J. Gegenberg and G. Kunstatter, Phys. Rev. D 47, R4192 (1993).

Physical Review D

Export citation

Export citation

Observables for two-dimensional black holes

Abstract

References (17)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation