Extremal limits and black hole entropy

Abstract

Taking the extremal limit of a non-extremal Reissner-Nordström 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 $Ad{S}_2\times S^2$. In other words, the approach to extremality is not continuous, as the non-extremal Reissner-Nordström 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.

10 pages, 3 figures. Minor corrections and added references

References in corpus (8)

• The Kerr/CFT Correspondence
• CFT Duals for Extreme Black Holes
• Kerr-AdS/CFT Correspondence in Diverse Dimensions
• Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1
• Euclidean Wormholes in String Theory
• Black hole entropy from entanglement: A review
• Thermodynamics at the BPS bound for Black Holes in AdS
• Euclidean analysis of the entropy functional formalism

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