Static, Spherically Symmetric, Anisotropic Stars in General Relativity

This work investigates the structure of static, spherically symmetric stellar objects considering pressure anisotropywithin the framework of General Relativity. A novel theoretical approach is presented in which the thermodynamicpressure of an Equation of State (EoS) is consistently identified with the tangential pressure. This assignmentis derived from the fundamental property of the EoS as a relation characterized by the absence of pressuregradients in its reference state, which remains preserved in the tangential plane of the stellar configuration dueto spherical symmetry. The radial pressure, in contrast, acts as a dynamical response to gravitational equilibrium.The field equations are formulated including a cosmological constant, and a detailed theoretical scheme fordetermining the metric functions as well as the mass and pressure profiles is derived. With regard to numericalintegration, the adaptation of the internal solution to the external Kottler spacetime using an auxiliary metricand the subsequent rescaling procedure are explained. Finally, the physical viability of the resulting model isdiscussed, emphasizing that the use of a realistic EoS for the tangential component inherently ensures thestability of the configuration as a direct consequence of the relativistic field equations.