Quantum thermodynamics in the interior of a Schwarzschild black-hole

Abstract

We study space-time back-reaction configuration in the interior of a Schwarzschild Black-Hole (B-H) using Relativistic Quantum Geometry described in (Ridao and Bellini 2015 Astrophys. Space Sci. 357 94) and (Ridao and Bellini 2015 Phys. Lett. B 751 565). We found discrete energy levels for a scalar field from a polynomial condition for Heun Confluent functions expanded around the Schwarzschild radius. From the solutions it is obtained that the uncertainty principle is valid for each energy level of space-time, in the form: En rsh,n=h/2. Temperature, entropy and the B-H mass are dependent on the number of states in the B-H, such that the Bekenstein-Hawking (BH) results are obtained in a limit case.