Particle motion around luminous neutron stars: Effects of deviation from Schwarzschild spacetime

We study trajectories of test particles around a luminous, static, spherically symmetric neutron star, under the combined influence of gravity and radiation. In general relativity, for Schwarzschild spacetime, an equilibrium sphere (the Eddington capture sphere) is formed for near-Eddington luminosities. We generalize these results to a broad class of static, spherical spacetimes. We also study the dynamics of particles in a strong radiation field in spherical spacetimes. The results are illustrated for two cases, Reissner-Nordstr"om spacetime of a charged spherical object in general relativity and Kehagias-Sfetsos spacetime, arising from the Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity theory. Our findings apply to neutron stars under gravitational field equations different from the vacuum Einstein field equations of general relativity, such as in modified theories of gravity, the only requirement being that test particles follow geodesics in the absence of the radiation field. The effects that we describe are, in principle, measurable through observations of x-ray bursts of neutron stars. Hence, detailed future studies could use such observations to test gravity theories in the strong-field regime, provided that the impact of the spacetime geometry can be disentangled from the astrophysical uncertainties.