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

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 $\nu \to 0$. 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.