Near-Extremal Freudenthal Duality

TL;DR

This paper extends Freudenthal duality, originally a symmetry of extremal black hole entropy, to near-extremal black holes, establishing a unique, analytical duality that relates black holes with different small temperatures but identical entropy.

Contribution

It introduces a consistent, unique generalization of Freudenthal duality to near-extremal black holes within a Jackiw-Teitelboim gravity framework.

Findings

Near-extremal Freudenthal duality relates black holes with different temperatures but same entropy.

The duality is shown to be analytical and unique using Descartes' rule of signs and Sturm's Theorem.

The formulation applies to black holes in Maxwell-Einstein-scalar theories in four dimensions.

Abstract

Freudenthal duality is, as of now, the unique non-linear map on electric-magnetic (e.m.) charges which is a symmetry of the Bekenstein-Hawking entropy of extremal black holes in Maxwell-Einstein-scalar theories in four space-time dimensions. In this paper, we present a consistent generalization of Freudenthal duality to near-extremal black holes, whose entropy is obtained within a Jackiw-Teitelboim gravity upon dimensional reduction. We name such a generalization near-extremal Freudenthal duality. Upon such a duality, two near-extremal black holes with two different (and both small) temperatures have the same entropy when their e.m. charges are related by a Freudenthal transformation. By exploiting Descartes' rule of signs as well as Sturm's Theorem, we show that our formulation of the near-extremal Freudenthal duality is analytical and unique.