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

• Main Authors: Cruz, Claudio Nassif, Santos, Rodrigo Francisco dos, FariaJr, A. C. Amaro de
• Format: Journal Article
• Language: English
• Published: 17-10-2020
• Subjects: Physics - General Physics
• DOI: 10.48550/arxiv.2009.03737

Physics of the Dark Universe, Vol. 27, 100454, p.1-10 (2020). OA
in: https://www.sciencedirect.com/science/article/pii/S2212686419303553 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
$R_S$ for a given coexistence radius $R_{coexistence}$ slightly larger than
$R_S$ and slightly smaller than the core radius $R_{core}$ of GBEC, where the
metric of the repulsive sector (core of GBEC) would diverge for $r=R_{core}$,
so that for such a given radius of phase coexistence $R_S<R_{coexistence}
<R_{core}$, both divergences at $R_S$ of Schwarzschild metric and at $R_{core}$
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 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.