Gravastars in $f(R,\,\Sigma ,\,T)$ strong-gravity and antigravity theories

Abstract

The aim of this manuscript is to investigate the gravastar model using the $f(R,\,\Sigma ,\,T)$ strong-gravity and anti-gravity theories, which is posited as a substitute for black holes. The gravastar consists of three regions: the interior, intermediate shell and exterior regions. Inside the interior region, the pressure is equal to the negative density, creating a repulsive force across the thin spherical shell. This shell comprises ultra-relativistic plasma fluids. The Zel'dovich conjecture assumes that the pressure is proportional to the matter–energy density, counterbalancing the repulsive force from the interior region. The exterior region is completely vacuumed and can be defined using a generalised form of the Schwarzschild solution. By applying these specifications, we arrive at numerous precise and singularity-free solutions for the gravastar. These solutions possess several physically valid features within an alternative gravity framework, specifically $f(R,\,\Sigma ,\,T)$ strong-gravity and anti-gravity. The gravitational Lagrangian is derived from an arbitrary function of the torsion scalar $\Sigma$ and the trace of the energy–momentum tensor $T$. In light of $f(R,\,\Sigma ,\,T)$ recent developments, we can now provide insight into the inner region of the gravastar by considering the interplay between gravity, strong gravity and antigravity forces, which arise from the torsion effect. This approach allows us to analyse important properties that characterise the shell region, such as the proper length, energy content and entropy. Furthermore, the junction, energy and boundary conditions necessary for the production of the thin shell are also discussed in detail. The analysis reveals that the matter density and pressure in the interior region remain constant, while the ultra-relativistic fluid within the shell is denser at the outer boundary than in the inner one. Additionally, the proper length of the shell gradually increases from the interior junction to the exterior junction. Overall, these findings shed light on the mechanisms that govern the behaviour of the gravastar and provide valuable insights into the fundamental principles that govern gravitation and its effects on the Universe.