Einstein-Born-Infeld-AdS Kara Deliklerinin termodinamiğinin Hamilton-Jacobi formülasyonu

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 and was applied to chargeless, non-rotating black holes in the same work. In this thesis we apply the formalism to charged, non-rotating black holes using the Born-Infeld theory and a negative cosmological constant. We fi rst review the basics of the causal structure of spacetime, black holes and in particular the Reissner-Nordstr öm black hole. Then we introduce the concepts related to the thermodynamics of black holes such as surface gravity and conserved Komar charges, and discuss the laws of black hole mechanics. We then review the contact geometric formulation of thermodynamics and the formalism developed by Rajeev. Lastly, we give the charged, non-rotating, asymptotically AdS black hole solution in the Einstein-Born-Infeld theory, derive the Hamilton-Jacobi equation and fi nd its most general solution. We show that there exist solutions which are distinct from the equations of state of the Einstein-Born-Infeld-AdS black hole. The meaning of these solutions is discussed.