Quark stars with isotropic matter in Ho\v{r}ava gravity and Einstein-{\ae}ther theory

TL;DR

This paper investigates the structure of non-rotating, isotropic quark stars within Lorentz-violating gravity theories, deriving generalized hydrostatic equations and analyzing how deviations from general relativity affect star properties.

Contribution

It introduces generalized structure equations for quark stars in Hořava gravity and Einstein-{ }ther theory, incorporating a deviation parameter and analyzing its effects on stellar characteristics.

Findings

Mass-radius relations depend on the deviation parameter $ u$.

Energy conditions and stability criteria are satisfied.

The generalized equations recover standard TOV equations when $ u ightarrow 0$.

Abstract

We study non-rotating and isotropic strange quark stars in Lorentz-violating theories of gravity, and in particular in Ho\v{r}ava gravity and Einstein-{\ae}ther theory. For quark matter we adopt both linear and non-linear equations of state, corresponding to the MIT bag model and colour flavour locked state, respectively. The new structure equations describing hydrostatic equilibrium generalize the usual Tolman-Oppenheimer-Volkoff (TOV) equations of Einstein's general relativity. A dimensionless parameter $\nu$ measures the deviation from the standard TOV equations, which are recovered in the limit $\nu \rightarrow 0$. We compute the mass, the radius as well as the compactness of the stars, and we show graphically the impact of the parameter $\nu$ on the mass-to-radius profiles for different equations of state describing quark matter. The energy conditions and stability criteria are also considered, and they are all found to be fulfilled.