Tidal stabilization of rigidly rotating, fully relativistic neutron stars

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 $\delta M(\mathcal{Q},R)$ 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 $R,\mathrm{}(d/dR)\mathrm{}\left[\delta M\right(\mathcal{Q},R)/{\mathcal{Q}}^2]<0\mathrm{}$ (where, as $R$ changes, the star’s structure is changed in accordance with the star’s fundamental mode of radial oscillation). If $\mathrm{}(d/dR)\mathrm{}\left[\delta M\right(\mathcal{Q},R)/{\mathcal{Q}}^2]$ 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.