Gravitational Field of Spherical Branes

TL;DR

This paper analyzes the gravitational properties of spherical branes in five-dimensional Anti-de Sitter space, revealing their negative active gravitational mass and potential for trapping fields, with explicit coordinate transformations provided.

Contribution

It presents an analytic form of coordinate transformations specific to five dimensions and demonstrates the negative gravitational mass of spherical branes, indicating their repulsive nature.

Findings

Spherical branes in 5D AdS have negative active gravitational mass.

The metric describes black hole interiors on both sides of the brane.

Explicit coordinate transformations from Schwarzschild to co-moving frame are derived.

Abstract

The warped solution of Einstein's equations corresponding to the spherical brane in five-dimensional AdS is considered. This metric represents interiors of black holes on both sides of the brane and can provide gravitational trapping of physical fields on the shell. It is found the analytic form of the coordinate transformations from the Schwartschild to co-moving frame that exists only in five dimensions. It is shown that in the static coordinates active gravitational mass of the spherical brane, in agreement with Tolman's formula, is negative, i.e. such objects are gravitationally repulsive.