On the effect of anisotropy on stellar models

Abstract

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 = G M/c 2 R, 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 ≤ 0.2073450586, and in particular for the maximum value of u n ∈ [−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.

Quintessences compact star with Durgapal potential

“…38,39 In our case, the parameter µ ∈ (0, 1] has an interval of values, which is consistent with the possibility that the matter is formed by a mixture of particles like quarks, neutrons and electrons and not only by one type of them. On the other hand, as it has been argued in a previous investigation report 35 and following this idea, other investigation works have been written, 32,34 the structure of the state equation for the tangential pressure is proposed to describe how the quintessence could disturb a perfect fluid.…”

“…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.…”

“…In different works, the possible behavior of the interior of some stars has been described through models with anisotropic pressures and this has shown that the observational results match those expected and obtained by a theoretical models, it has also been shown the importance that the anisotropy has in the description of physically acceptable models. 7 The type of matter that could conform the stars with density greater than the nuclear density is expected to contain neutrons, quarks as well as electrons, although not only one of these components. The stars where their matter is mainly formed by quarks may be more compact than the stars constituted mainly by neutrons, in addition to this, it has been speculated on the possibility that the quintessence matter is also part of the star's interior, this type of matter could counteract the effect of the gravitational attraction because, as it is known, it generates negative pressures.…”

“…28,29 Within the variety of compact stars with quintessence, [30][31][32] one of the most approached is that associated to the MIT Bag model, 33,34 for this case, starting from a state equation associated to the ordinary matter and considering the effect of the quintessence, it has been shown that the geometry of the solutions for Einstein's equations with perfect fluid works for describing compact stars with quintessence. 35 However, it is to be expected that the ordinary matter that conforms a star is not only constituted by quarks and that depending on its mass, radius, density or compactness its state equation may differ. Taking this into account, and as to generalize from previous works, 35 in this work, we present a compact star constituted by quintessence and ordinary matter with radial and tangential pressures described by the state equa-…”

“…35 However, it is to be expected that the ordinary matter that conforms a star is not only constituted by quarks and that depending on its mass, radius, density or compactness its state equation may differ. Taking this into account, and as to generalize from previous works, 35 in this work, we present a compact star constituted by quintessence and ordinary matter with radial and tangential pressures described by the state equa-…”