Volume 125, Number 1, January 2019
|Number of page(s)||5|
|Published online||29 January 2019|
Hamilton-Jacobi formulation of the thermodynamics of Einstein-Born-Infeld-AdS black holes
Department of Physics, Koç University - 34450 Istanbul, Turkey
Received: 14 December 2018
Accepted: 10 January 2019
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 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 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.
PACS: 04.70.Bw – Classical black holes / 02.40.Hw – Classical differential geometry / 05.70.Ce – Thermodynamic functions and equations of state
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