Lorentz violation with an invariant minimum speed as foundation of the Gravitational Bose Einstein Condensate of a Dark Energy Star

• Published in: PHYSICS OF THE DARK UNIVERSE Vol. 27; p. 100454
• Main Authors: Cruz, Cláudio Nassif, dos Santos, Rodrigo Francisco, Amaro de Faria, A.C.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-01-2020
• Subjects: Dark energy star; Gravitational Bose-Einstein condensate; Lorentz violation; Minimum speed; Phase transition; Planck length; Vacuum energy; Gravitational Bose-Einstein condensate; Planck length; Dark energy star; Minimum speed; Vacuum energy; Phase transition; Lorentz violation
• ISSN: 2212-6864; 2212-6864
• DOI: 10.1016/j.dark.2019.100454

We aim to search for the connection between the spacetime with an invariant minimum speed so-called Symmetrical Special Relativity (SSR) with Lorentz violation and the Gravitational Bose Einstein Condensate (GBEC) as the central core of a star of gravitational vacuum (gravastar), where one normally introduces a cosmological constant for representing an anti-gravity. This usual model of gravastar with an equation of state (EOS) for vacuum energy inside the core will be generalized for many modes of vacuum (dark energy star) in order to circumvent the embarrassment generated by the horizon singularity as the final stage of a gravitational collapse. In the place of the problem of a singularity of an event horizon, we introduce a phase transition between gravity and anti-gravity before reaching the Schwarzschild (divergent) radius RS for a given coexistence radius Rcoexistence slightly larger than RS and slightly smaller than the core radius Rcore of GBEC, where the metric of the repulsive sector (core of GBEC) would diverge for r=Rcore, so that for such a given radius of phase coexistence RS<Rcoexistence<Rcore, both divergences at RS of Schwarzschild metric (a fine shell of baryonic matter involving the core of GBEC) and at Rcore of the repulsive core are eliminated, thus preventing the formation of the event horizon. So the causal structure of SSR helps us to elucidate such puzzle of singularity of event horizon by also providing a quantum interpretation for GBEC and thus by explaining the origin of a strong anisotropy due to the minimum speed (dark cone) that leads to the phase transition gravity/anti-gravity during the collapse of the star. Furthermore, due to the absence of an event horizon of black hole (BH) where any signal cannot propagate, the new collapsed structure presents a signal propagation in its region of coexistence of phases where the coexistence metric does not diverge, thus leading to emission of radiation.