Thermodynamics of dyonic black holes in minimal supergravity

TL;DR

This paper analyzes the thermodynamics of dyonic black holes in five-dimensional supergravity, resolving inconsistencies in the first law and deriving the Smarr formula using advanced formalisms, supported by numerical validation.

Contribution

It introduces a consistent thermodynamic framework for dyonic black holes in supergravity, correcting previous discrepancies and deriving key relations using the Iyer-Wald formalism.

Findings

Resolved the inconsistency in the first law of thermodynamics for dyonic black holes.

Derived the Smarr formula consistent with the first law.

Validated the theoretical results with numerical tests.

Abstract

Thermodynamics of black holes offers a promising avenue for exploring the quantum nature of black holes and quantum gravity. In this Letter, we investigate the thermodynamic properties of dyonic black holes in the five-dimensional Einstein-Maxwell-Chern-Simons theory, obtained from IIB supergravity. We demonstrate that the standard form of the first law of thermodynamics is inconsistent with the quantum statistical relation widely adopted in black hole physics. By employing the on-shell variation of the Euclidean action and the Iyer-Wald formalism, we resolve this discrepancy and derive both the standard form of the first law and Smarr formula for the dyonic black holes. Furthermore, our findings are corroborated by numerical tests and are consistent with general hydrodynamic expectations.