Relativistic anisotropic fluid spheres satisfying a non-linear equation of state
Francisco Tello‐Ortiz, Manuel Malaver, Ángel Rincón, Y. Gómez-Leyton
Abstract
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 $$e^{2\lambda (r)}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>λ</mml:mi><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:math> and an equation of state. Specifically, the so-called modified generalized Chaplygin equation of state with $$\omega =1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ω</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> 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 $$\rho $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ρ</mml:mi></mml:math> , the radial $$p_{r}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>p</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:math> , and tangential $$p_{t}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>p</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:math> pressures as well as the anisotropy factor $$\Delta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Δ</mml:mi></mml:math> . 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 $$R=9.5\ [km]$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mn>9.5</mml:mn><mml:mspace/><mml:mo>[</mml:mo><mml:mi>k</mml:mi><mml:mi>m</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:math> . 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.