Thermodynamic Study of Higher Dimensional Black Holes through Exponential Entropy Models

Abstract

In this thesis, we work on thermodynamics of black holes via expo- nentially corrected entropies. Exponential corrections are applied to the entropy of 5D charged AdS black hole solutions that are found in Einstein Gauss Bonnet gravity and the nonlinear electrodynamics. Also, three dif- ferent versions of 5D charged AdS black hole are considered by assuming q ! 0; k ! 0 and ¯ ! 0 (where q is charge, k is non-linear parameter and ¯ is coupling constant). For these black holes, extended phase space (where cosmological constant is interpreted as pressure) and ¯rst law of the black hole thermodynamics are demonstrated. Further, the thermal sta- bility/instability, ¯rst/second order phase transitions for these black holes are investigated through the behavior of heat capacity at constant pressure, Gibbs free energy, Helmoltz free energy and the trace of the Hessian matrix in the presence of exponentially corrected entropies.