Geometric Aspects of Extremal Kerr Black Hole Entropy

Ecaterina Howard

Department of Physics and Astronomy, Macquarie University, Sydney, Australia.

DOI: 10.4236/jmp.2013.43050                

Abstract

Extreme Black Holes is an important theoretical laboratory for exploring the nature of entropy. We suggest that this unusual nature of the extremal limit could explain the entropy of extremal Kerr black holes. The time-independence of the extremal black hole, the zero surface gravity, the zero entropy and the absence of a bifurcate Killing horizon are all related properties that define and reduce to one single unique feature of the extremal Kerr spacetime. We suggest the presence of a true geometric discontinuity as the underlying cause of a vanishing entropy.

Keywords

Bifurcate Killing Horizon; Extremal Kerr Black Hole; Black Hole Entropy

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. D. Bekenstein, “Black Holes and Entropy,” Physical Review D, Vol. 7, No. 8, 1973, pp. 2333-2346. doi:10.1103/PhysRevD.7.2333
[2]	S. W. Hawking and G. F. R. Ellis, “The Large Scale Structure of Space-Time,” Cambridge University Press, Cambridge, 1973.
[3]	B. O’Neill, “The Geometry of Kerr Black Holes,” A K Peters, Wellesley, Massachusetts, 1995.
[4]	S. Chandrashekar, “The Mathematical Theory of Black Holes,” Clarendon Press, Oxford, 1983.
[5]	C. W. Misner, K. S. Thorne and J. A. Wheeler, “Gravitation,” W. H. Freeman, San Francisco, 1973.
[6]	R. Geroch, “Limits of Spacetimes,” Communications in Mathematical Physics, Vol. 13, No. 3, 1969, pp. 180-193. doi:10.1007/BF01645486
[7]	I. Racz, “Does the Third Law of Black Hole Thermodynamics Really Have a Serious Failure?” Classical and Quantum Gravity, Vol. 17, No. 20, 2000, pp. 4353-4356. doi:10.1088/0264-9381/17/20/410
[8]	S.W. Hawking, et al., “Entropy, Area, and Black Hole Pairs,” Physical Review D, Vol. 51, No. 8, 1995, pp. 4302-4314. doi:10.1103/PhysRevD.51.4302
[9]	J. Bardeen and G. T. Horowitz, “The extreme Kerr throat geometry: A vacuum analog of AdS2 ? S2,” Physical Review D, Vol. 60, No. 10, 1999, Article ID: 104030. doi:10.1103/PhysRevD.60.104030
[10]	A. J. Amsel, G. T. Horowitz, D. Marolf and M. M. Roberts, “No Dynamics in the Extremal Kerr Throat,” Journal of High Energy Physics, Vol. 2009, 2009, p. 044. doi:10.1088/1126-6708/2009/09/044
[11]	R. M. Wald, “General Relativity,” The University of Chicago Press, Chicago, 1984.
[12]	R. M. Wald, “Black Hole Entropy Is the Noether Charge,” Physical Review D, Vol. D48, No. 8, 1993, pp. 3427-3431. doi:10.1103/PhysRevD.48.R3427