Non-trivial class of anisotropic compact stellar model in Rastall gravity

TL;DR

This paper explores anisotropic stellar models within Rastall gravity, demonstrating their physical viability, differences from General Relativity, and potential to describe neutron and quark stars without assuming an equation of state.

Contribution

It introduces a non-trivial class of anisotropic stellar models in Rastall gravity, showing their compatibility with observational data and highlighting differences from GR.

Findings

Rastall gravity models produce similar anisotropy as GR for static stars.

The models fit observational data from 20 pulsars, including neutron and quark star candidates.

An upper bound on compactness aligns with the Buchdahl limit, with a maximum mass of 3.53 solar masses.

Abstract

We investigated Rastall gravity, for an anisotropic star with a static spherical symmetry, whereas the matter-geometry coupling as assumed in Rastall Theory (RT) is expected to play a crucial role in differentiating RT from General Relativity (GR). Indeed, all the obtained results confirm that RT is not equivalent to GR, however, it produces the same amount of anisotropy as GR for static spherically symmetric stellar models. We used the observational constraints on the mass and the radius of the pulsar \textit{Her X-1} to determine the model parameters confirming the physical viability of the model. We found that the matter-geometry coupling in RT allows slightly less size than GR for a given mass. We confirmed the model viability via other twenty pulsars' observations. Utilizing the strong energy condition we determined an upper bound on compactness $U_\text{max}\sim 0.603$, in agreement with the Buchdahl limit, whereas Rastall parameter $\epsilon=-0.1$. For a surface density compatible with a neutron core at nuclear saturation density, the mass-radius curve allows masses up to $3.53 M_\odot$. We note that there is no equation of state is assumed, however, the model fits well with a linear behavior. We split the twenty pulsars into four groups according to the boundary densities. Three groups are compatible with neutron cores while one group fits perfectly with higher boundary density $8\times 10^{14}$ g/cm$^3$ which suggests that those pulsars may have quark-gluon cores.