A proof of the reverse isoperimetric inequality using a geometric-analytic approach

TL;DR

This paper proves the reverse isoperimetric inequality for black holes in Einstein gravity using a novel geometric-analytic approach, highlighting gravity's fundamental role in this thermodynamic property.

Contribution

It introduces a new proof of the reverse isoperimetric inequality for AdS black holes in Einstein gravity, connecting geometric-analytic methods with gravitational background structures.

Findings

Reversal of the isoperimetric inequality is rooted in Einstein gravity's structure.

The proof applies to black holes in dimensions D ≥ 4.

Gravity fundamentally influences the reverse isoperimetric property.

Abstract

We present a proof of the reverse isoperimetric inequality - a central conjecture in extended black hole thermodynamics - for black holes in Einstein gravity with $D \geq 4$, employing a two-pronged geometric-analytic method. Our analysis shows that the reversal of the usual isoperimetric inequality originates from the structure of curved backgrounds governed by Einstein's equations, thereby underscoring the fundamental role of gravity in the reverse isoperimetric property of AdS black hole horizons.