Emergent AdS_3 in the Zero Entropy Extremal Black Holes

TL;DR

This paper explores how AdS_3 geometries emerge in the zero entropy limit of extremal black holes, revealing new insights into their near horizon structure and implications for the Kerr/CFT correspondence.

Contribution

It demonstrates the emergence of AdS_3 structures in zero entropy extremal black holes and analyzes the conditions and implications of this phenomenon.

Findings

AdS_3 geometry appears in the zero entropy limit.

Conditions for regularity of near horizon geometries are derived.

Implications for Kerr/CFT correspondence are discussed.

Abstract

We investigate the zero entropy limit of the near horizon geometries of D=4 and D=5 general extremal black holes with SL(2,R)xU(1)^{D-3} symmetry. We derive some conditions on the geometries from expectation of regularity. We then show that an AdS_3 structure emerges in a certain scaling limit, though the periodicity shrinks to zero. We present some examples to see the above concretely. We also comment on some implications to the Kerr/CFT correspondence.