Physical process version of the first law of thermodynamics for black holes in Einstein-Maxwell axion-dilaton gravity

TL;DR

This paper derives a physical version of the first law of black hole thermodynamics within Einstein-Maxwell axion-dilaton gravity, linking variations in mass, angular momentum, and charge to matter perturbations, supporting cosmic censorship.

Contribution

It provides the first derivation of the physical first law of black hole dynamics in Einstein-Maxwell axion-dilaton gravity, a low-energy string theory limit.

Findings

Derived general formulae for mass and angular momentum variations.

Expressed variations in terms of matter energy-momentum and charge current.

Supported the cosmic censorship conjecture.

Abstract

We derive general formulae for the first order variation of the ADM mass, angular momentum for linear perturbations of a stationary background in Einstein-Maxwell axion-dilaton gravity being the low-energy limit of the heterotic string theory. All these variations were expressed in terms of the perturbed matter energy momentum tensor and the perturbed charge current density. Combining these expressions we reached to the form of the {\it physical version} of the first law of black hole dynamics for the stationary black holes in the considered theory being the strong support for the cosmic censorship.