Searching Exact Solutions for Compact Stars in Braneworld: a conjecture

TL;DR

This paper develops a method to find exact solutions for non-uniform stellar distributions in braneworld models, overcoming the non-closure problem of braneworld equations by imposing a physically motivated constraint.

Contribution

It introduces a new constraint that reduces degrees of freedom in braneworld stellar solutions, enabling the derivation of exact, physically acceptable internal solutions.

Findings

A constraint linking braneworld solutions to general relativity limits.

An exact internal solution for non-uniform stars in braneworlds.

Bulk corrections do not induce anisotropic effects on the brane.

Abstract

In the context of the braneworld, a method to find consistent solutions to Einstein's field equations in the interior of a spherically symmetric, static and non uniform stellar distribution with Weyl stresses is developed. This method, based in the fact that any braneworld stellar solution must have the general relativity solution as a limit, produces a constraint which reduces the degrees of freedom on the brane. Hence the non locality and non closure of the braneworld equations can be overcome. The constraint found is physically interpreted as a necessary condition to regain general relativity, and a particular solution for it is used to find an exact and physically acceptable analytical internal solution to no-uniform stellar distributions on the brane. It is shown that such an exact solution is possible due to the fact that bulk corrections to pressure, density and a metric component are a null source of anisotropic effects on the brane. A conjecture is proposed about the possibility of finding physically relevant exact solutions to non-uniform stellar distributions on the brane.