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Journal Article

A quasi-radial stability criterion for rotating relativistic stars

MPS-Authors

Takami,  Kentaro
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons20670

Rezzolla,  Luciano
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1105.3069
(Preprint), 239KB

MNRAS416_L1.pdf
(Any fulltext), 926KB

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Citation

Takami, K., Rezzolla, L., & Yoshida, S. (2011). A quasi-radial stability criterion for rotating relativistic stars. Monthly Notices of the Royal Astronomical Society, 416, L1-L5. doi:10.1111/j.1745-3933.2011.01085.x.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000E-EB76-E
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.