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Extremal limits and black hole entropy

Sean M. Carroll
(
- Caltech
)
,
Matthew C. Johnson
(
- Caltech
)
,
Lisa Randall
(
- Harvard U., Phys. Dept.
)

Jan, 2009

11 pages

Published in:

JHEP 11 (2009) 109

e-Print:

0901.0931 [hep-th]

DOI:

10.1088/1126-6708/2009/11/109

Report number:

CALT-68-2717

View in:

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Abstract: (arXiv)

Taking the extremal limit of a non-extremal Reissner-Nordstr\'om black hole (by externally varying the mass or charge), the region between the inner and outer event horizons experiences an interesting fate -- while this region is absent in the extremal case, it does not disappear in the extremal limit but rather approaches a patch of

AdS_2\times S^2

. In other words, the approach to extremality is not continuous, as the non-extremal Reissner-Nordstr\'om solution splits into two spacetimes at extremality: an extremal black hole and a disconnected

AdS

space. We suggest that the unusual nature of this limit may help in understanding the entropy of extremal black holes.

black hole: entropy
black hole: Reissner-Nordstroem
space-time: anti-de Sitter
Einstein-Maxwell equation: solution
compactification

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