Stellar stability in brane-worlds revisited

TL;DR

This paper analyzes the stability conditions of brane-world stars under minimal assumptions, establishing bounds on their compactness and showing that such stars have a Schwarzschild exterior.

Contribution

It provides a general stability analysis for brane stars with simplified nonlocal effects and identifies the Germani-Maartens solution as an upper bound for compactness.

Findings

Germani-Maartens solution bounds star compactness

Minimal setup implies Schwarzschild exterior

Stability conditions derived for brane stars

Abstract

We consider here the general conditions for the stability of brane stars that obey a so called a "minimal setup": the nonlocal anisotropic stress and energy flux are everywhere absent, and the only permitted Weyl correction is the interior solution of the nonlocal energy density. Along with a series of simple conditions, we show that the Germani-Maartens solution with a constant density sets up the upper bound for the compactness of that particular class of brane stars. The general demonstration is based upon the properties of the interior solutions of the stars, although we also show that the minimal setup implies a Schwarzschild exterior.