Physical Existence of Relativistic Stellar Models within the context of Anisotropic Matter Distribution
M. Sharif, Tayyab Naseer, Hira Shadab
TL;DR
This paper investigates the physical existence of relativistic stellar configurations with anisotropic matter in static, spherically symmetric spacetimes. It derives the Einstein field equations for an anisotropic fluid, defines the Misner–Sharp mass via $m'(r)=4\pi r^2\rho$, and introduces the anisotropy measure $\Pi(r)=8\pi(p_t-p_r)$. By establishing physical acceptability criteria (regularity, energy conditions, causality, and stability), it constructs two analytical solutions constrained by the radial metric function and anisotropy; Model I, in particular, yields a closed-form $A_1(r)$ and explicit density and pressure profiles, with constants fixed by boundary matching to the Schwarzschild exterior. Graphical analysis using observed stellar radii and masses supports the physical viability and underscores the advantageous role of anisotropy in compact interiors.
Abstract
Two distinct non-singular interior models that describe anisotropic spherical configurations are presented in this work. We develop the Einstein field equations and the associated mass function in accordance with a static spherical spacetime. We then discuss certain requirements that must be satisfied for compact models to be physically validated. Two distinct limitations are taken into account to solve the field equations, including different forms of the radial geometric component and anisotropy, which ultimately leads to a couple of relativistic models. In both cases, solving the differential equations result in the appearance of integration constants. By equating the Schwarzschild exterior metric and spherical interior line element on the interface, these constants are explicitly obtained. The disappearance of the radial pressure on the hypersurface is also used in this context. We further use estimated radii and masses of six different stars to graphically visualize the physical properties of new solutions. Both of our models are deduced to be well-aligned with all physical requirements, indicating the superiority of the presence of anisotropy in compact stellar interiors over the perfect isotropic fluid content.