Quantum mechanics of a black hole: Effect of correlation energy on Schwarzschild radius and Hawking temperature

Abstract

Using a single particle density distribution for the self-gravitating quantum particles that form an interacting N-particle system which ultimately forms a black hole, we from a condensed matter point of view derive the expressions of the Schwarzschild radius and the Hawking temperature. Including the quantum mechanical exchange correlation energy for the particles, we find small corrections to the above two physical quantities. The approximate expression of ground state energy and the numerical coefficient of the formula for Hawking temperature provide the hint to enable us to propose an exact expression for the ground state energy of the system.