A perfect fluid model for compact stars

TL;DR

This paper introduces a new exact interior solution for compact stars within general relativity, modeling neutron stars and quark stars with a perfect fluid that matches observed properties of specific stars.

Contribution

It presents a novel perfect fluid interior solution based on a gravitational redshift factor, applicable to modeling neutron and quark stars with realistic density and pressure profiles.

Findings

Model describes neutron star PSR J0348+0432 accurately

Density and pressure are monotonic decreasing functions

Sound speed remains below light speed

Abstract

In the framework of Einstein's the theory of general relativity we present a new interior solution with a perfect fluid, this is constructed from the proposal of a gravitational redshift factor. The geometry is regular and its density and pressure are monotonic decrescent functions, furthermore the sound speed is smaller than the light speed and monotonic crescent. The solution depends on a parameter $w \in (0, 2.0375509325]$ related to the compactness of the star $u = GM/c^2 R$, the maximum value $u = 0.2660858316$ which allow to describe compact stars like quark stars or neutron stars. Although there is a diversity of stars for which the model can be used, we only apply this solution to describe the interior of a neutron star PSR J0348$+$0432. According to the observations, it is known that its mass $M = (2.01 \pm 0.04)M_{\odot}$ and its radius is between 12.062Km and 12.957Km, so the value of the compactness is in the range $u \in [0.2244845, 0.2509338]$. In addition to the decreasing behavior of the mentioned pressure and density functions, the results are consistent with the density values range typical of neutron stars and the maximal central density of the star result to be 1.283818 $\times 10^{18} Kg/m^{3}$.