# Volumetric Maxima to be Attained by a Nonstatic Black Hole

## TL;DR

This paper introduces a modified Eddington-Finkelstein metric satisfying Einstein's equations, calculates the interior volume and entropy of a black hole based on this metric, and explores their time dependence and thermodynamic properties.

## Contribution

It presents a new metric that satisfies Einstein's equations and derives novel expressions for black hole interior volume and entropy with explicit time dependence.

## Key findings

- Interior volume depends on a time function, differing from previous models.
- Entropy of the interior volume is proportional to the square of a time-dependent function.
- Thermodynamic properties of the black hole interior are analyzed with the new metric.

## Abstract

Christodoulou and Rovelli have calculated maximal interior volume of a Schwarzschild black hole which linearly grows with time. Recently, the entropy of interior volume in a Schwarzschild black hole has also been calculated. In this article, the Eddington-Finkelstein metric is slightly modified. This modified metric satisfies Einstein's equations. The interior volume of a black hole is also calculated with the modified metric. The volume explicitly depends on a function of time, different from the Christodoulou and Rovelli volume. Also entropy is calculated corresponding to the volume which is proportional to the square of a function of time and thermodynamics is studied.