Strange stars in the presence of quintessence

Abstract

In this work, starting from the solution for Einstein’s equations in a static and spherically symmetrical space time, we present a quintessence model $\rho _\mathrm{q}$ which describes compact stars. The model for the star has anisotropic pressures given by the state equations $P_\mathrm{r}=c^2(\rho -\rho _\mathrm{b})$ and $P_\mathrm{t}=c^2(\rho -\rho _\mathrm{b})-3(1+w)c^2\rho _\mathrm{q}/2$, where $\rho _\mathrm{b}$ is the density on the surface of the star and the parameter of the quintessence matter is such that $-1<w<-\frac{1}{3}$. The densities $(\rho ,\rho _\mathrm{q})$ and pressures $(P_\mathrm{r},P_\mathrm{t})$ are positive, finite and monotonically decreasing as functions of the radial distance. The solution satisfies the condition of causality, and the maximum compactness of the model $u=GM/c^2R=0.31311406$ is the result of satisfying the stability condition $v_\mathrm{t}^2-v_\mathrm{r}^2<0$; for this value, the tangential speed of sound in the center is equal to the speed of light. On the other hand, the maximum density of the quintessence occurs for the compactness $u=0.2669552108$; meanwhile, the maximum values of the other functions are obtained for the maximum compactness. As a verification of the applicability of our model, considering the observational data of the strange star candidate 4U 1608–52, with mass $M=(1.74\pm 0.14)M_\odot$ and radius $R=(9.83\pm 1)$ km, we described this for some masses and radii $(1.87M_\odot ,8.83$ km), $(1.60M_\odot ,8.83$ km) and $(1.60M_\odot ,10.83$ km), and the greatest central density $\rho _\mathrm{c}= 1.85943 10^{18}{\mathrm{kg/m}^3}$ was obtained for the greatest compactness $u=0.3126838187$ and is independent of the quintessence parameter; however, this value does have an effect on the value of the tangential speed of sound.