Impact of $f(\Re,\mathcal{T}^{2})$ Theory on Stable Finch-Skea Gravastar Model

Abstract: This paper examines the structure of a gravitationally vacuum star (also known as gravastar) in the background of ${f}(\Re,\mathcal{T}^{2})$ theory. This hypothetical object can be treated as a substitute of a black hole, with three regions: (i) the internal region, (ii) the intrinsic shell and (iii) the outer region. We examine these geometries using Finch-Skea metric for radial metric component along with particular $f(\Re,\mathcal{T}^{2})$ model. We determine singularity-free solution for both the inner as well as thin-shell domains. The smooth matching of the interior region with external Schwarzschild spacetime is obtained through Israel matching constraints. Finally, we study various characteristics of gravastar domains including equation of state parameter, proper length, entropy, energy as well as surface redshift. It is found that the compact gravastar structure is a viable alternate to the black hole in the perspective of this gravity.