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

2025/08/18 by Kumar, Naman
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2508.13235

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 ≥ 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.

Citations

• Quantum inequalities for quantum black holes
• ArXiv
• Holographic heat engines
• The cosmological constant and black-hole thermodynamic potentials
• Enthalpy and the mechanics of AdS black holes
• Minimal Varieties in Riemannian Manifolds

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