Gravitational pressure on event horizons and thermodynamics in the teleparallel framework

TL;DR

This paper explores gravitational pressure and black hole thermodynamics within the teleparallel gravity framework, deriving new expressions for pressure and thermodynamic relations without relying on horizon area variations.

Contribution

It introduces a novel approach to black hole thermodynamics using teleparallel gravity, defining gravitational pressure and energy without area considerations.

Findings

Derived gravitational pressure on Kerr black hole horizon.

Formulated thermodynamic relation TdS = dE + pdV in teleparallel gravity.

Results align qualitatively with standard black hole thermodynamics.

Abstract

The concept of gravitational pressure is naturally defined in the context of the teleparallel equivalent of general relativity. Together with the definition of gravitational energy, we investigate the thermodynamics of rotating black holes in the teleparallel framework. We obtain the value of the gravitational pressure over the external event horizon of the Kerr black hole, and write an expression for the thermodynamic relation $TdS =dE + pdV$, where the variations refer to the Penrose process for the Kerr black hole. We employ only the notions of gravitational energy and pressure that arise in teleparallel gravity, and do not make any consideration of the area or the variation of the area of the event horizon. However, our results are qualitatively similar to the standard expression of the literature.