Compact stellar models with quasi-local anisotropy

Abstract

In this article, we introduce a new compact stellar model by deriving simple, exact analytical solutions to the Einstein field equations in the presence of anisotropy. We focus on an anisotropic star, employing the quasi-local method suggested by Horvat et al. (Class Quantum Gravity 28: 025009, 2011) to describe fluid anisotropy within a spherical symmetry using quasi-local variables, whose values are determined from physics within a very small region around a spacetime point. We then ensure smooth matching between the interior spherically symmetric spacetime and the exterior Schwarzschild spacetime. To confirm the physical validity of our model, we analyze various parameters both analytically and graphically. To further support our solution’s applicability to compact stellar objects, we use observational data from the well-known pulsar \(4U 1608-52\) in our graphical analysis.