Quantum thermodynamics in the interior of a Schwarzschild B-H

We study the interior of a Schwarzschild Black-Hole (B-H) using Relativistic Quantum Geometry described in \cite{rb} and \cite{rb1}. We found discrete energy levels for a scalar field from a polynomial condition for Heun Confluent functions expanded around the Schwarzschild radius. From the solution...

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Bibliographic Details
Published in:arXiv.org 2019-12
Main Authors: Musmarra, Juan Ignacio, Bellini, Mauricio, Anabitarte, Mariano
Format: Article
Language:English
Subjects:
Energy levels
Functions (mathematics)
Mathematical analysis
Phase transitions
Polynomials
Online Access:Get full text
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Summary:We study the interior of a Schwarzschild Black-Hole (B-H) using Relativistic Quantum Geometry described in \cite{rb} and \cite{rb1}. 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: \(E_n\, r_{sh,n}=\hbar/2\). 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.
ISSN:2331-8422
DOI:10.48550/arxiv.1904.11599