Entropy for the Interior of a Schwarzschild Black Hole Assuming the Mass is Increasing With Time

TL;DR

This paper calculates the entropy inside a Schwarzschild black hole with increasing mass, showing it aligns with Bekenstein-Hawking entropy and obeys thermodynamic laws, including relativistic and scalar charge effects.

Contribution

It introduces a model for black hole interior entropy with increasing mass, incorporating relativistic corrections and scalar charge effects, extending previous thermodynamic analyses.

Findings

Entropy proportional to Bekenstein-Hawking expression

Entropy satisfies the second law of thermodynamics

Relativistic and scalar charge effects influence thermodynamic properties

Abstract

Black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons. Here we calculate the entropy corresponding to the interior of a Schwarzschild black hole for massless modes, assuming the mass of the black hole increasing with time. We find that the entropy is proportional to the Bekenstein-Hawking expression. Also, we can see that the evaluated entropy satisfies the second law of thermodynamics. Using the thermodynamic law we get a relation between temperature and inverse temperature. The special relativistic corrections to thermodynamic quantities are considered. The change in thermodynamic properties are analyzed when the velocity of the considered system is comparable to the speed of light. The effect of presence of scalar charge is incorporated.