Non-uniform Braneworld Stars: an Exact Solution

TL;DR

This paper presents the first exact interior solution for a static, non-uniform braneworld star, revealing how bulk gravity influences the star's internal structure and matching conditions with an exterior Reissner-Nordström-like solution.

Contribution

It provides the first exact interior solution for a non-uniform braneworld star considering both local and non-local bulk effects.

Findings

Bulk Weyl scalar ${\

}U(r)$ is always negative inside the star.

Bulk gravity induces anisotropy with physically acceptable behavior inside the star.

Abstract

The first exact interior solution to Einstein's field equations for a static and non-uniform braneworld star with local and non-local bulk terms is presented. It is shown that the bulk Weyl scalar ${\cal U}(r)$ is always negative inside the stellar distribution, in consequence it reduces both the effective density and the effective pressure. It is found that the anisotropy generated by bulk gravity effect has an acceptable physical behaviour inside the distribution. Using a Reissner-N\"{o}rdstrom-like exterior solution, the effects of bulk gravity on pressure and density are found through matching conditions.