ENTROPIES AND THERMODYNAMIC STABILITY OF BLACK HOLES

Abstract

In this thesis, we investigates thermodynamic stability of black holes, including to the Schwarzschild-de Sitter black hole and Schwarzschild-like black holes in the Horndeski theory. We study thermodynamics of the vector-tensor Horndeski black holes by using a proper black hole’s entropy, that is the Wald entropy. The vectortensor Horndeski black hole is classified into two types, viz. magnetic-Horndeski black hole (MHBH) and electric-Horndeski black hole (EHBH). Since the solution of MHBH is the analytic one, it allows us to investigate thermodynamic stability together with the linear stability. For the EHBH, the solution is obtained from numerical method. The thermodynamic stability can be considered solely. MHBH and EHBH are thermodynamic stable with the similar conditions for value of coupling constant. In case of the Schwarzschild-de Sitter black hole, we consider the black hole with other statistics’ representation. The Rényi entropy is one that we have chosen, because it can serve the zeroth law compatibility of thermodynamics. By extending the phase space, the Schwarzschild-de Sitter black hole can be thermodynamically stable in this representation.