An interior solution with perfect fluid

Abstract

Starting from the construction of a solution for Einstein’s equations with a perfect fluid for a static spherically symmetric spacetime, we present a model for stars with a compactness rate of [Formula: see text]. The model is physically acceptable, that is to say, its geometry is non-singular and does not have an event horizon, pressure and speed of sound are bounded functions, positive and monotonically decreasing as function of the radial coordinate, also the speed of sound is lower than the speed of light. While it is shown that the adiabatic index [Formula: see text], which guarantees the stability of the solution. In a complementary manner, numerical data are presented considering the star PSR J0737-3039A with observational mass of [Formula: see text], for the value of compactness [Formula: see text], which implies the radius [Formula: see text] and the range of the density [Formula: see text] [Formula: see text], where [Formula: see text] and [Formula: see text] are the central density and the surface density, respectively. This range is consistent with the expected values; as such, the model presented allows to describe this type of stars.

An Einstein-Maxwell interior solution obeying Karmarkar condition

“…So in the charged case the hydrostatic equilibrium is given by the attractive effect of the gravitational force F g , the repulsive hydrostatic force due to the pressure gradient F h and the electric force F e resulting of the presence of the charge, each one of these terms have already been mentioned in the Eqs. ( 8) and (9). The graphic behaviour of these forces is shown in the Fig.…”

“…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

“…Theorem 1 could be applied to the set of known regular solutions for a perfect fluid [49,[52][53][54][55] and we obtain for each one of these a model that tentatively describes stars formed by quintessence and MIT Bag matter. The existence of these with the equations for the radial and tangential pressures given by (7) and (8) is a new theoretical proposal presented in this work., Its possible physical existence is justified by the astrophysics observations related to the accelerated expansion of the universe.…”

Relativistic charged stellar modeling with a perfect fluid sphere

“…Inside of the proposals that take into account the presence of the charge we have different approaches, which can be categorized in two cases, (a) generalizations starting from chargeless solutions to a case in which there is a charge, which are models for which in the absence of charge the chargeless case is recovered and (b) charged models that are not reduced to a chargeless case. Inside of the first class, there have been presented a variety of generalizations from the models of chargeless perfect fluid to the case of a charged perfect fluid, as are the interior solutions of Tolman IV [24,25], Tolman VI, [24,26,27], Tolman VII [24,28,29], Wyman-Adler [30][31][32][33], Buchdahl [34,35], Kuchowicz [36,37], Heintzmann [38,39], Durgapal (n = 4) [40,41], Durgapal (n = 5) [40,42], Vaidya-Tikekar [43][44][45][46], Durgapal-Fuloria [47,48], Knutsen [49,50], Pant [51][52][53], Estevez-Delgado [54,55] among others [13,[56][57][58][59][60]. In the first works, this reduction of a charged model to a chargeless model was an imposed requirement in the construction of charged interior solutions, however, rec...…”