The solution of the Einstein equation in the interior of the black holes by using arbitrary distribution functions

TL;DR

This paper derives solutions to Einstein's equations inside black holes using various distribution functions and calculates related thermodynamic properties like Hawking temperature and heat capacity.

Contribution

It introduces a novel approach of applying arbitrary distribution functions to solve Einstein's equations within black holes, expanding the analytical methods in black hole physics.

Findings

Solutions obtained for different distribution functions

Calculated Hawking temperature and heat capacity

Analyzed thermodynamic properties of black hole horizons

Abstract

The aim of this paper is to obtain the solution of the Einstein equation in the interior of the black holes by using arbitrary distribution functions; corresponding to Gaussian, Rayleigh, Maxwell-Boltzmann and non-Gaussian distributions. Also we calculate the Hawking temperature, the mass and heat capacity for cosmological horizon and the black hole horizon.