Tidal stabilization of rigidly rotating, fully relativistic neutron stars

Abstract

It is shown analytically that an external tidal gravitational field increases the secular stability of a fully general relativistic, rigidly rotating neutron star that is near marginal stability, protecting it against gravitational collapse. This stabilization is shown to result from the simple fact that the energy δM(Q,R) required to raise a tide on such a star, divided by the square of the tide’s quadrupole moment Q, is a decreasing function of the star’s radius R, (d/dR)[δM(Q,R)/Q2]<0 (where, as R changes, the star’s structure is changed in accordance with the star’s fundamental mode of radial oscillation). If (d/dR)[δM(Q,R)/Q2] were positive, the tidal coupling would destabilize the star. As an application, a rigidly rotating, marginally secularly stable neutron star in an inspiraling binary system will be protected against secular collapse, and against dynamical collapse, by tidal interaction with its companion. The “local-asymptotic-rest-frame” tools used in the analysis are somewhat unusual and may be powerful in other studies of neutron stars and black holes interacting with an external environment. As a by-product of the analysis, in an appendix the influence of tidal interactions on mass-energy conservation is elucidated.