sudhaker upadhyay

In this paper, we consider an $\alpha^{\prime}$ corrected Reissner-Nordstr\"{o}m AdS black hole to study thermodynamics. We study the $P-V$ criticality and thermodynamical stability of black hole. We obtained a first-order phase transition which may be interpreted as the large/small black hole phase transition. Therefore, we obtained a van der Waals behaviour and obtained critical points. Finally, we calculate quantum work which is used to resolve the information loss paradox.

In this paper, we study the Hawking radiation for a dilatonic BTZ black hole solution and derive the transmission probability of tunnelling through the barrier of the event horizon. Furthermore, we discuss the black hole chemistry of the black hole solution under the effect of thermal fluctuation and find that the thermal fluctuation plays a significant role for the black hole with small horizon radius.

In this paper, we consider non-minimally coupled gravity model. We choose some suitable new variables and achieve the new Hamiltonian and Lagrangian which have harmonic oscillator form. The corresponding Lagrangian is deformed by non-commutative geometry. In order to have solution for the bouncing universe we specify the potential in the equation state. In that case we draw the equation of state in terms of time and show that the equation of state cross $-1$. Such bouncing behavior lead us to apply some conditions on $theta$ and $beta$ from non-commutative geometry. Here, also we can check the stability of system due to deformation of the non-minimally coupled to gravity model. In order to examine thestability of system we obtain the variation of pressure with respect to density energy. Also, we draw the variation of pressure with respect to energy density and show the condition of stability.

We present the thermodynamics of a charged and rotating BTZ black holes here. In particular, we derive expressions for various macroscopic thermal quantities such as entropy, Hawking temperature, Helmholtz free energy, internal energy, enthalpy, Gibbs free energy, and specific heat.To study the effects of small statistical thermal fluctuations around the equilibrium on thermodynamics, we calculated the leading-order corrections to the variousthermodynamical potentials of charged and rotating BTZ black hole and do comparative analysis for the fixed values of charge and angular momentum.