Freudenthal duality of near-extremal black holes and Jackiw-Teitelboim gravity

TL;DR

This paper investigates how Freudenthal duality affects the entropy of near-extremal black holes within supergravity, revealing that the duality's invariance breaks down when applied to near-extremal entropy, unlike the extremal case.

Contribution

It introduces a reduction of four-dimensional supergravity to a JT gravity-like model to analyze near-extremal entropy and examines the limitations of F-duality in this regime.

Findings

F-duality preserves extremal black hole entropy and solutions.

F-duality does not preserve near-extremal entropy when applied through near-extremal solutions.

Near-extremal entropy is sensitive to the duality operation, breaking the invariance seen in extremal cases.

Abstract

Freudenthal duality (F-duality), an anti-involution of charge vectors keep the entropy and attractor solutions invariant for an extremal supersymmetric black hole. In this paper, we analyze the effect of F-duality on the entropy of a near-extremal $STU$ black hole in $\mathcal{N}=2$ ungauged, four-dimensional supergravity. We consider double-extremal black holes, whose attractor solutions are fixed in terms of the black hole charges throughout the moduli space. It is well known that JT gravity governs the dynamics of the near-horizon regions of higher dimensional, near-extremal black holes. Owing to this fact, we reduce the four-dimensional supergravity theory to two dimensions to construct a Jackiw-Teitelboim (JT) gravity like model and compute the near-extremal entropy. We then analyze the effect of F-duality on this entropy. We show that the F-duality breaks down for the case of near-extremal solutions if one considers the duality operation generated through near-extremal entropy rather than the extremal one.