On the effect of anisotropy on stellar models

The relevance of anisotropy in compact models is shown by the construction of a stellar model, this can influence the behavior of density, pressure and speed of sound in such grade that if the anisotropy disappear it could produce a regular model of perfect fluid which is not physically acceptable. The present anisotropic model has dependence in two parameters n associated with the anisotropy and w related with the rate of compactness \(u=GM/c^2R\), this is regular and physically acceptable. That is the speed of sound is positive and lower than the light speed, the density as well as radial and tangential pressure are monotonic decrescent functions. The compactness values for which the radial and tangential speed of sound are monotonic decrescent functions and the solution is potentially stable occurs for \(u\le 0.2073450586\), and in particular for the maximum value of u \(n\in -0.771108398\), \(-0.231572621]\). While if \(n=1\) we get a model of perfect regular fluid but the density and speed of sound can not be both positive at the origin, so the solution is not physically acceptable in the absence of anisotropic pressures.