Instability windows of Chandrasekhar-Friedman-Schutz instability

Rotating, self-gravitating mass of incompressible ideal fluid possesses an axially symmetric equilibrium configuration known as the Maclaurin spheroid. Fluid viscosity causes dissipation-induced instability of this equilibrium [1,2]. Chandrasekhar [3] discovered that radiation reaction force due to emission of gravitational waves could lead to a radiative instability of the Maclaurin spheroids. In the presence of both viscosity and resistivity the ratio of these two dissipative forces plays a crucial role [4], determining the instability window for the Chandrasekhar-Friedman-Schutz (CFS) instability. The CFS instability is commonly accepted nowadays as one of the main triggers of gravitational radiation from single neutron stars that is the next goal for the existing (LIGO, Virgo) and planned (LISA) detectors of gravitational waves [5,6]. Perturbation theory for eigenvalues in combination with numerical methods was proposed for calculation of instability windows of the CFS instability already in [3,4,7]. We are extending this approach to the multiple-parameter case by adopting the methodology of [8,9] to get better approximations and to put the CFS to the general context of the dissipation-induced instability theory.
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