The correspondence between thermodynamic curvature and isoperimetric theorem from ultraspinning black hole

TL;DR

This paper explores the relationship between thermodynamic curvature and the isoperimetric theorem in ultraspinning black holes, revealing negative curvature indicating attractive interactions and a proportionality between curvature remnants and inverse entropy.

Contribution

It establishes a preliminary link between thermodynamic curvature and the isoperimetric theorem in ultraspinning black holes, highlighting the sign of curvature and its relation to black hole entropy.

Findings

Thermodynamic curvature of ultraspinning black holes is negative.

Extreme black holes exhibit curvature remnants proportional to inverse entropy.

The study suggests an attractive interaction between black hole molecules.

Abstract

In this paper, a preliminary correspondence between the thermodynamic curvature and the isoperimetric theorem is established from a $4$-dimensional ultraspinning black hole. We find that the thermodynamic curvature of ultraspinning black hole is negative which means the ultraspinning black hole is likely to present an attractive between its molecules phenomenologically if we accept the analogical observation that the thermodynamic curvature reflects the interaction between molecules in a black hole system. Meanwhile we obtain a general conclusion that the thermodynamic curvature of the extreme black hole of the super-entropic black hole has a (positive or negative) remnant approximately proportional to the reciprocal of entropy of the black hole.