Relativistic Anisotropic Fluid Spheres Satisfying a Non-Linear Equation of State

TL;DR

This paper presents a new relativistic anisotropic fluid sphere model satisfying a modified generalized Chaplygin equation of state, analyzing its physical properties and stability to suggest it could represent a quark star with dark energy.

Contribution

The work introduces a specific solution to Einstein's equations with a novel equation of state and performs a comprehensive physical and stability analysis.

Findings

Model is stable under adiabatic index criteria.

Configuration is in hydrostatic equilibrium.

Results suggest the structure could represent a quark star with dark energy.

Abstract

In this work, a spherically symmetric and static relativistic anisotropic fluid sphere solution of the Einstein field equations is provided. To build this particular model, we have imposed metric potential $e^{2\lambda(r)}$ and an equation of state. Specifically, the so-called modified generalized Chaplygin equation of state with $\omega=1$ and depending on two parameters, namely, $A$ and $B$. These ingredients close the problem, at least mathematically. However, to check the feasibility of the model, a complete physical analysis has been performed. Thus, we analyze the obtained geometry and the main physical observables, such as the density $\rho$, the radial $p_{r}$, and tangential $p_{t}$ pressures as well as the anisotropy factor $\Delta$. Besides, the stability of the system has been checked by means of the velocities of the pressure waves and the relativistic adiabatic index. It is found that the configuration is stable in considering the adiabatic index criteria and is under hydrostatic balance. Finally, to mimic a realistic compact object, we have imposed the radius to be $R=9.5\ [km]$. With this information and taking different values of the parameter $A$ the total mass of the object has been determined. The resulting numerical values for the principal variables of the model established that the structure could represent a quark (strange) star mixed with dark energy.