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

Understand

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.