Thermodynamics of Einstein-Maxwell-dilaton black hole in (2+1) dimensions

Abstract

Curvature in space time fabric arises by taking stress energy tensor as some source field. Motivation for using matter fields are their abundance in nature and Schwarszchild black hole is one of the most symmetric static massive solution of Einstein field equation. Many other solutions of Einstein field equation are also found by modifying Einstein’s action with some gauge fields and other theories. Effective theory can be arise if one takes higher energy theory such as string theory. Einstein’s action is naturally modified with some scalar-tensor superstring terms at sufficiently high energy scale. On taking low energy limit Einstein’s action is recovered with a dilaton scalar field which is coupled to gravity. In this thesis, we work on Einstein-Maxwell-Scalar theory in (2+1) dimensions that contains a scalar field coupled minimally to gravity and a potential that depends solely on scalar field. We obtained an exact solution containing a black hole with a regular horizon. Further, we also work on the thermodynamic properties of black hole and try to prove the First law of Thermodynamics for our solutions. • The first chapter give elementary details of Einstein’s equation and its solution. The brief description of Black hole with three characteristic properties: mass, charge and angular momentum is given in this chapter. • In the second chapter, the motivation for the project work, modification of Einstein’s action with Maxwell-Scalar terms and the equation of motions are given. • In the third chapter we work on the anastz in (2+1) dimensions and discussed various techniques used to obtained the exact solution of Einstein-Maxwell-Scalar gravity. The komar integral are used to prove first law of Black hole thermodynamics.