Tidal Stabilization of Rigidly Rotating, Fully Relativistic Neutron Stars

TL;DR

This paper demonstrates analytically that external tidal gravitational fields can enhance the stability of rotating neutron stars near collapse, potentially preventing their gravitational collapse during binary interactions.

Contribution

It introduces a novel analytical approach showing how tidal interactions stabilize relativistic neutron stars, with implications for binary systems and gravitational collapse prevention.

Findings

Tidal gravitational fields increase neutron star stability near collapse.

The energy required to raise a tide decreases with star radius, stabilizing the star.

Tidal interactions can prevent both secular and dynamical collapse in binary systems.

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 $\delta M(Q,R)$ 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 $R$, $(d/dR)[\delta M(Q,R)/Q^2]<0$ (where, as $R$ changes, the star's structure is changed in accord with the star's fundamental mode of radial oscillation). If $(d/dR)[\delta M(Q,R)/Q^2]$ 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 byproduct of the analysis, in an appendix the influence of tidal interactions on mass-energy conservation is elucidated.