Black hole thermodynamics

Abstract

We examine here the stability of black holes, in both way first is the thermodynamic way, by using the Hessian matrix of thermodynamic variables, useful in analyzing thermodynamic instability, and second is the dynamical way by perturbing the met ric of black brane/string given by Horowitz and Strominger and also perturbation of scalar fields and gauge fields in a supergravity Lagrangian using AdS/CFT argu ments, if the perturbation does not vanish we found the unstable modes in the form of dynamical instability. By comparing thermodynamical and dynamical instability it is conjectured by Gub ser and Mitra in his paper that black holes with a lack of thermodynamic stability often also lack stability against small perturbation i.e, dynamical instability, which is included as the central part of the whole work