Radiating sources in higher-dimensional gravity

TL;DR

This paper explores higher-dimensional gravity by deriving 4D solutions from a 5D metric, revealing models of dense astrophysical objects and heat flow using embedding theorems and induced matter formalism.

Contribution

It introduces a method to obtain 4D solutions from a 5D metric with spherical symmetry, including models with stiff matter and heat flow, expanding understanding of higher-dimensional gravitational sources.

Findings

Derived 4D solutions with stiff matter equation of state.

Obtained models with radial heat flow.

Close-to Schwarzschild approximation achieved.

Abstract

We study a time-dependent 5D metric which contains a static 4D sub-metric whose 3D part is spherically symmetric. An expansion in the metric coefficient allow us to obtain close-to Schwarzschild approximation to a class of spherically-symmetric solutions. Using Campbell's embedding theorem and the induced-matter formalism we obtain two 4D solutions. One describes a source with the stiff equation of state believed to be applicable to dense astrophysical objects, and the other describes a spherical source with a radial heat flow.