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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.
We show the relationship between the scalar kinematics potential of Symmetrical Special Relativity (SSR) and the ultra-referential of vacuum connected to an invariant minimum speed postulated by SSR. The property of the conformal metric of SSR is sho
We aim to investigate the theory of Lorentz violation with an invariant minimum speed so-called Symmetrical Special Relativity (SSR) from the viewpoint of its metric. Thus we should explore the nature of SSR-metric in order to understand the origin o
This work presents an experimental test of Lorentz invariance violation in the infrared (IR) regime by means of an invariant minimum speed in the spacetime and its effects on the time when an atomic clock given by a certain radioactive single-atom (e
We aim to search for a connection between an invariant minimum speed that breaks down the Lorentz symmetry and the Gravitational Bose Einstein Condensate (GBEC), which is the central core of a star of gravitating vacuum (Gravastar/Dark Energy Star) b
Partly motivated by recent proposals for the detection of gravitational waves, we study their interaction with Bose-Einstein condensates. For homogeneous condensates at rest, the gravitational wave does not directly create phonons (to lowest order),