Stability of the graviton Bose-Einstein condensate in the brane-world

TL;DR

This paper investigates the stability of graviton Bose-Einstein condensate stars within a brane-world scenario, linking stability conditions to the absence of singularities and information entropy critical points.

Contribution

It introduces a novel analysis of BEC stellar configurations in the brane-world context using the Minimal Geometric Deformation approach.

Findings

Identifies the critical stability region for BEC MGD stars.

Relates critical stellar densities to information entropy extrema.

Constrains brane tension based on singularity absence.

Abstract

We consider a solution of the effective four-dimensional Einstein equations, obtained from the general relativistic Schwarzschild metric through the principle of Minimal Geometric Deformation (MGD). Since the brane tension can, in general, introduce new singularities on a relativistic E\"otv\"os brane model in the MGD framework, we require the absence of observed singularities, in order to constrain the brane tension. We then study the corresponding Bose-Einstein condensate (BEC) gravitational system and determine the critical stability region of BEC MGD stellar configurations. Finally, the critical stellar densities are shown to be related with critical points of the information entropy.