Thermodynamics of Specific Black Holes

Abstract

In this thesis, we modify the first law of thermodynamics for regular black hole of non-minimal Einstein-Yang-Mill theory with gauge field of magnetic Wu-Yang type and a regular black hole, which is associated with cosmological constant by the surface tensions. The corresponding Smarr relations are also satisfied for them. The cosmological constant is taken as constant as well as variable (which is correlated with pressure). We calculate the Gibbs free energy to discuss the global stability of the above mentioned regular black holes in general relativity. At first, the cosmological constant is adopted as fixed and then as a variable, which is correlated with the pressure. The first law of thermodynamics is modified for both regular black holes, mentioned above, when the cosmological constant is treated as fixed and as a variable. Also, we investigate the thermodynamical properties and consider the logarithmic correction to entropy in order to analyze thermal fluctuations of two another regular black hole: 1) The AdS black hole in Born-Infeld massive gravity with a non-abelian hair. 2) The charged AdS black hole with a global monopole. We develop the many thermodynamical quantities such as entropy, temperature, pressure, heat capacity of a system at constant volume and pressure, ratio between the heat capacities at constant pressure and volume, the Gibbs free energy and the Helmholtz free energy for both black holes. We observe the critical behavior and phase transition and check the validity of the first law of thermodynamics. We observe the local stability and the global stability of the black holes in the grand canonical ensemble and canonical ensemble for the specific values of different parameters, such as, symmetry breaking parameter η and massive parameter m. ix