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

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.