A gravastar model with Durgapal—Fuloria metric potential

In this present work, we have proposed a novel gravastar model as a viable alternative model to the black hole(BH) theory by using the Durgapal-Fuloria metric potential in a $(3+1)$ dimensional framework which overcomes the central singularity and event horizon problem. Mazur and Motolla(M-M) introduced the idea of gravitational vacuum condensate star(gravastar) by studying the Bose–Einstein condensation in the gravitational systems. The gravastar solution featured an interior de-Sitter spacetime along with an external Schwarzschild space–time. A thin shell separates the de-Sitter interior from the exterior region. By utilizing the Durgapal-Fuloria metric potential, the other metric potential in the interior and the shell region have been determined that eliminates the singularity. We have examined the shell region comprising of ultra-relativistic plasma such as proper length, energy and entropy and they are found to be increasing with increasing thickness. Furthermore, we have analyzed the junction conditions that match the interior and the exterior spacetimes, it is observed that the surface energy density and surface pressure are decreasing with increasing thickness. The analysis of speed of sound predicts the stability of the gravastar model. Thus our results yield a complete family of exact solutions for the gravatsar, which are not only non-singular but also stable.