A generalized anisotropic model for super dense stars

Abstract

A static anisotropic relativistic fluid sphere model with regular geometry and finite hydrostatic functions is presented. In the interior of the sphere, the density, radial pressure and tangential pressure are positives, monotonically decreasing with increasing radius and the radial pressure vanishes at the surface of the matter distribution and is joined continuously to the exterior Schwarzschild’s solution at this surface. The speeds of the radial and tangential sound are positive and lower than the speed of light, that is, the causal condition is not violated, and also the behavior of these guarantees that the model is potentially stable. Furthermore, the range of the compactness ratio is characteristic of compact stars and it is shown that the effect of the anisotropy generates that the speed of the radial sound can behave as a function monotonically increasing or monotonically decreasing.