Hamilton-Jacobi Formulation of the Thermodynamics of Einstein-Born-Infeld-AdS Black Holes

TL;DR

This paper develops a Hamilton-Jacobi formalism for the thermodynamics of Einstein-Born-Infeld-AdS black holes, deriving the equations of state and exploring the space of solutions, including novel solutions beyond standard black hole thermodynamics.

Contribution

It extends the Hamilton-Jacobi thermodynamic formalism to charged Einstein-Born-Infeld-AdS black holes, deriving the general solution and analyzing its implications.

Findings

Derived the Hamilton-Jacobi equation for charged black holes with Born-Infeld electromagnetism.

Found the most general solution of the Hamilton-Jacobi equation.

Identified solutions that differ from standard black hole equations of state.

Abstract

A Hamilton-Jacobi formalism for thermodynamics was formulated by Rajeev [Ann. Phys. 323, 2265 (2008)] based on the contact structure of the odd dimensional thermodynamic phase space. This allows one to derive the equations of state of a family of substances by solving a Hamilton-Jacobi equation (HJE). In the same work it was applied to chargeless non-rotating black holes, and the use of Born-Infeld electromagnetism was proposed to apply it to charged black holes as well. This paper fulfills this suggestion by deriving the HJE for charged non-rotating black holes using Born-Infeld theory and a negative cosmological constant. The most general solution of this HJE is found. It is shown that there exists solutions which are distinct from the equations of state of the Einstein-Born-Infeld-AdS black hole. The meaning of these solutions is discussed.