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A<sc>bstract</sc> We examine the thermodynamics of a near-extremal Kerr black hole, and demonstrate that the geometry behaves as an ordinary quantum system with a vanishingly small degeneracy at low temperatures. This is in contrast with the classical analysis, which instead predicts a macroscopic entropy for the extremal Kerr black hole. Our results follow from a careful analysis of the gravitational path integral. Specifically, the low temperature canonical partition function behaves as$$ Z\sim {T}^{\frac{3}{2}}\ {e}^{S_0+c\log {S}_0} $$ , withS0the classical degeneracy andca numerical coefficient we compute. This is in line with the general expectations for non-supersymmetric near-extremal black hole thermodynamics, as has been clarified in the recent past, although cases without spherical symmetry have not yet been fully analyzed until now. We also point out some curious features relating to the rotational zero modes of the near-extremal Kerr black hole background that affects the coefficientc. This raises a puzzle when considering similar black holes in string theory. Our results generalize to other rotating black holes, as we briefly exemplify.
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The Entropy of Black Holes
Abstract The remarkable connection between black holes and thermodynamics provides the most significant clues that we currently possess to the nature of black holes in a quantum theory of gravity. The key clue is the formula for the entropy of a black hole. I briefly review some recent work that provides an expression for a dynamical correction to the entropy of a black hole and briefly discuss some of the implications of this new formula for entropy.
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- Award ID(s):
- 2403584
- PAR ID:
- 10591722
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- General Relativity and Gravitation
- Volume:
- 57
- Issue:
- 5
- ISSN:
- 0001-7701
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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