An anisotropic model for stars

Abstract

A stellar model with anisotropic pressure is constructed and analyzed, the metric components that describe the geometry and the source of matter satisfy Einstein’s equations and both are finite inside the star. In addition, density and pressure are decreasing monotone functions of the radial distance. The speed of sound is positive and less than the speed of light, furthermore the model is potentially stable. The model allows describing compact objects with compactness of [Formula: see text] and as a result of the anisotropic value there is a range of values of the central density, in particular for the maximum value of compactness a star with [Formula: see text] and a value of anisotropic parameter [Formula: see text] we get a stellar radius of [Formula: see text] and a central density [Formula: see text]. The above makes the solution a physically realistic model that can be used to describe dense objects such as neutron stars whose characteristic density is of the order of nuclear density.

An Einstein-Maxwell interior solution obeying Karmarkar condition

“…Solutions with perfect fluid tend to be more complicated to obtain than charged solutions or anisotropic solutions, i.e., fluids that present differences between the radial and tangential pressures, since the number of restrictions that can be imposed is lower for the case of a perfect fluid. Even the solutions with perfect fluid [1][2][3][4][5][6][7][8][9][10] can be used as seed solutions to obtain generalizations to the charged [11][12][13][14][15][16][17] or anisotropic [18][19][20][21][22][23][24] cases. There is also a method to obtain the solution of a perfect fluid from a seed solution of perfect fluid, this mechanism utilizes the existence of a second order differential equation that relates the metric coefficients g tt and g rr , although this one can only generate an exact new solution, return to an exact solution that was already known or it can even be that the resulting integral equation does not admit a primitive function [25,26].…”

On quintessence star model and strange star

“…On the other hand there have been some approaches at a stellar level to describe compact objects [20][21][22][23], considering that the interior of the stars is formed by ordinary neutral matter [24][25][26][27][28][29][30], ordinary charged matter [31][32][33][34][35][36][37], and also by sources which are a combination of ordinary matter and quintessence dark energy, consistent with neutron stars [38]. Neutron or quark stars are not exclusively composed of neutrons or quarks, respectively, but rather these stars are formed predominantly by one of those particles.…”

Quintessences compact star with Durgapal potential

“…For example, it is known that when the internal density is greater than the nuclear density, there is the possibility that the radial and tangential pressures are different from each other, which would indicate that its interior is not necessarily formed by a perfect fluid, but instead by an anisotropic fluid. 1 The description of the stars formed by anisotropic fluids has been studied since the last century [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and one of the consequences is that it would allow to describe stars with a compactness value greater than the Buchdahl limit u < 4/9, [19][20][21][22] this presents itself even in the case of the anisotropic model with constant density. 23 The generalization of the Buchdahl limit for the anisotropic case only requires conditions on the behavior of the function of density, the pressure and its coupling with the exterior geometry described by the Schwarzschild solution 20 and not on a specific form of the state equation.…”