Can Extremal Black Holes Have Non-Zero Entropy?
Abstract
We give several pieces of evidence to show that extremal black holes cannot be obtained as limits of non-extremal black holes. We review arguments in the literature alleging that the entropy of extremal black holes is zero, while that of near-extremal ones obey the Bekenstein-Hawking formula. However, from the counting of degeneracy of quantum (BPS) states of string theory the entropy of extremal stringy black holes has been claimed to obey the area law. An attempt is made to reconcile these arguments. In particular, we propose that stringy effects modify the topology of the two dimensional Euclidean section of the metric near the horizon such that the area law remains valid. While this modification preserves the extremality condition, it endows the black hole with a non-zero Hawking temperature.Keywords
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