Hamilton-Jacobi formulation of the thermodynamics of Einstein-Born-Infeld-AdS black holes

Abstract

A Hamilton-Jacobi formalism for thermodynamics was formulated by Rajeev (Ann. Phys., 323 (2008) 2265) 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 changeless 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 the Born-Infeld theory and a negative cosmological constant. The most general solution of this HJE is found. It is shown that there exist solutions which are distinct from the equations of state of the Einstein-Born-Infeld-AdS (EBIAdS) black hole. The meaning of these solutions is discussed.