A quasi-radial stability criterion for rotating relativistic stars

TL;DR

This paper challenges previous assumptions by showing that the neutral-stability point for rotating relativistic stars does not coincide with the turning point, providing a new criterion for assessing their dynamical stability through full general relativity calculations.

Contribution

The study introduces a revised stability criterion for rotating relativistic stars, demonstrating that the neutral-stability point differs from the classical turning point and validating it with numerical simulations.

Findings

The neutral-stability point differs from the turning point in rotating stars.

Full general relativity calculations of the $F$-mode frequency reveal new stability insights.

Numerical simulations confirm the effectiveness of the new stability criterion.

Abstract

The stability properties of relativistic stars against gravitational collapse to black hole is a classical problem in general relativity. A sufficient criterion for secular instability was established by Friedman, Ipser and Sorkin (1988), who proved that a sequence of uniformly rotating barotropic stars is secularly unstable on one side of a turning point and then argued that a stronger result should hold: that the sequence should be stable on the opposite side, with the turning point marking the onset of secular instability. We show here that this expectation is not met. By computing in full general relativity the $F$-mode frequency for a large number of rotating stars, we show that the neutral-stability point, i.e., where the frequency becomes zero, differs from the turning point for rotating stars. Using numerical simulations we validate that the new criterion can be used to assess the dynamical stability of relativistic rotating stars.