Compact stars in Rastall gravity: hydrostatic equilibrium and radial pulsations

Abstract

Within the context of Rastall gravity, we investigate the hydrostatic equilibrium and dynamical stability against radial pulsations of compact stars, where a free parameter \(\beta \) measures the deviations from General Relativity (GR). We derive both the modified Tolman–Oppenheimer–Volkoff (TOV) equations and the Sturm–Liouville differential equation governing the adiabatic radial oscillations. Such equations are solved numerically in order to obtain the compact-star properties for two realistic equations of state (EoSs). For hadronic matter, the fundamental mode frequency \(\omega _0\) becomes unstable almost at the critical central energy density corresponding to the maximum gravitational mass. However, for quark matter, where larger values of \(\vert \beta \vert \) are required to observe appreciable changes in the mass-radius diagram, there exist stable stars after the maximum-mass configuration for negative values of \(\beta \) . Using an independent analysis, our results reveal that the emergence of a cusp can be used as a criterion to indicate the onset of instability when the binding energy is plotted as a function of the proper mass. Specifically, we find that the central-density value where the binding energy is a minimum corresponds precisely to \(\omega _0^2 =0\) .