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arXiv · 0901.0931

Extremal limits and black hole entropy

Sean M. Carroll·Matthew C. Johnson·Lisa Randall
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Abstract

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.

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Sean M. Carroll, Matthew C. Johnson, Lisa Randall. 2009-01-08. Extremal limits and black hole entropy. https://doi.org/10.1088/1126-6708/2009/11/109

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