The resonance found for incompressible stars persists for compressible polytropic stars with stiff equations of state, but its radius shrinks as the polytropic index grows, and the second-order resonance disappears for n=2.
Relativistic Roche problem for stars in precessing orbits around a spinning black hole
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Tidal disruptions of stars on the equatorial plane orbiting Kerr black holes have been widely studied. However thus far, there have been fewer studies of stars in inclined precessing orbits around a Kerr black hole. In this paper, we use the tensor virial equations to show the presence of possible resonances in these systems for typical physical parameters of black hole-neutron star binaries in close orbits or of a white dwarf/an ordinary star orbiting a supermassive black hole. This suggests the presence of a new instability before the tidal disruption limit is encountered in such systems.
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Resonances of compressible stars in precessing orbits around a spinning black hole
The resonance found for incompressible stars persists for compressible polytropic stars with stiff equations of state, but its radius shrinks as the polytropic index grows, and the second-order resonance disappears for n=2.