On the r-mode spectrum of relativistic stars

Abstract

We present a mathematically rigorous proof that the r-mode spectrum of relativistic stars to the rotational lowest order has a continuous part. A rigorous definition of this spectrum is given in terms of the spectrum of a continuous linear operator. This study verifies earlier results by Kojima (1998) about the nature of the r-mode spectrum.

6 pages, no figures

References in corpus (3)

• Gravitational waves from hot young rapidly rotating neutron stars
• On the relevance of the r-mode instability for accreting neutron stars and white dwarfs
• Generalized r-Modes of the Maclaurin Spheroids

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• The Science of the Einstein Telescope
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• Rotational modes of non-isentropic stars and the gravitational radiation driven instability
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• Relativistic r-modes in Slowly Rotating Neutron Stars: Numerical Analysis in the Cowling Approximation
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• Vorticity affects the stability of neutron stars
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• Robertson-Walker fluid sources endowed with rotation characterised by quadratic terms in angular velocity parameter