Interior properties of five-dimensional Schwarzschild black hole

TL;DR

This paper explores the internal structure of a five-dimensional Schwarzschild black hole, deriving equations of state and analyzing uniform density configurations using a five-dimensional generalization of known relativistic models.

Contribution

It introduces a five-dimensional version of the TOV equation and analyzes interior solutions for five-dimensional Schwarzschild black holes.

Findings

Derived a five-dimensional hydrostatic equilibrium equation.

Obtained a general relativistic pressure expression for uniform density configurations.

Provided insights into the internal properties of higher-dimensional black holes.

Abstract

We investigate inner structure of Schwarzschild black hole on a five-dimensional spacetime S^3xR^2. To do this, we exploit a f\"unfbein scheme. In particular, we construct an equation of state of hydrostatic equilibrium for the five-dimensional Schwarzschild black hole, which is a five-dimensional version of the Tolman-Oppenheimer-Volkoff equation on four-dimensional manifold. We also investigate uniform density interior configuration of the five-dimensional black hole which consists of incompressible fluid of density, to find a general relativistic expression for pressure.