Spherically Symmetric de Sitter Solution of Black Holes

TL;DR

This paper derives a spherically symmetric de Sitter black hole solution using various distribution functions, analyzing its thermodynamic properties, energy conditions, and regularity to contribute to understanding black hole models in de Sitter space.

Contribution

It introduces a general distribution function framework for black hole solutions and examines their thermodynamic and geometric properties, including energy conditions and regularity.

Findings

Thermodynamic variables like Hawking temperature and entropy are characterized.

The solution satisfies the strong energy condition.

The curvature invariants indicate the solution's regularity.

Abstract

In this study we obtain the solution of the spherically symmetric de Sitter solution of black holes using a general form of distribution functions which include Gaussian, Rayleigh, and Maxwell-Boltzmann distribution as a special case. We investigate the properties of thermodynamics variables such as the Hawking temperature, the entropy, the mass and the heat capacity of black holes. Moreover, we show that the strong energy condition which includes the null energy condition is satisfied. Finally, we show the regularity of the solution by calculating the scalar curvature and invariant curvature in general distribution form.