Static, Spherically Symmetric, Anisotropic Stars in General Relativity

This work investigates the structure of static, spherically symmetric stellar objects considering pressure anisotropy
within the framework of General Relativity. A novel theoretical approach is presented in which the thermodynamic
pressure of an Equation of State (EoS) is consistently identified with the tangential pressure. This assignment
is derived from the fundamental property of the EoS as a relation characterized by the absence of pressure
gradients in its reference state, which remains preserved in the tangential plane of the stellar configuration due
to 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 for
determining the metric functions as well as the mass and pressure profiles is derived. With regard to numerical
integration, the adaptation of the internal solution to the external Kottler spacetime using an auxiliary metric
and the subsequent rescaling procedure are explained. Finally, the physical viability of the resulting model is
discussed, emphasizing that the use of a realistic EoS for the tangential component inherently ensures the
stability of the configuration as a direct consequence of the relativistic field equations.