Theoretical study on five dimensional AdS black holes with dilaton backreaction

Abstract

We classify the AdS black holes into extremal and non-extremal black holes by their asymptotic geometries near the horizons. We find that the extremality of the black holes are related to the Hawking temperature. In particular we study AdS black holes solutions of five dimensional Hilbert-Einstein action with a cosmological constant and a dilaton, which is minimally coupled to gravity. We consider type of solutions or black holes which are static and spherically symmetric. By completing the effective Lagrangian into square, or can be called the Hamiltonian method, we write the equation of motions in terms of BPS equations which are of first order differential equations. We find that trivial dilaton contribution gives non-extremal black hole solution while the non-trivial dilaton does not give black hole solution.