Geometrical and hydrodynamic aspects of five-dimensional Schwarzschild black hole

TL;DR

This paper explores the geometry, thermodynamics, and particle dynamics of a five-dimensional Schwarzschild black hole, revealing differences from four-dimensional cases and analyzing effective potentials on a restricted brane.

Contribution

It provides a detailed geometric and thermodynamic analysis of five-dimensional Schwarzschild black holes, including their embedding in higher-dimensional space and particle behavior on a brane.

Findings

Different Hawking temperature from four-dimensional black holes

Radial Einstein equation form remains consistent with four dimensions

Effective potential analysis on a restricted brane

Abstract

Exploiting the five-dimensional Schwarzschild black hole, we study the geometrical natures of the higher dimensional black hole to yield the (6+1) dimensional global embedding Minkowski space structure. We next obtain the Hawking temperature on this five-dimensional manifold, whose result is different from the four-dimensional one. On the contrary, the radial component of the Einstein equation for the massive particles or photons on the five-dimensional spacetime is shown to have the same form as the four-dimensional black hole one. Moreover, we construct the effective potential on equatorial plane of the restricted three-brane to investigate the behavior of the particles or photons on this restricted brane.