Regularizing the r-mode problem for nonbarotropic relativistic stars

Abstract

We present results for r-modes of relativistic nonbarotropic stars. We show that the main differential equation, which is formally singular at lowest order in the slow-rotation expansion, can be regularized if one considers the initial value problem rather than the normal mode problem. However, a more physically motivated way to regularize the problem is to include higher order terms. This allows us to develop a practical approach for solving the problem and we provide results that support earlier conclusions obtained for uniform density stars. In particular, we show that there will exist a single r-mode for each permissible combination of $l$ and $m$. We discuss these results and provide some caveats regarding their usefulness for estimates of gravitational-radiation reaction timescales. The close connection between the seemingly singular relativistic r-mode problem and issues arising because of the presence of corotation points in differentially rotating stars is also clarified.

considerably revised version, to appear in Class. Quantum. Grav

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Cited by in corpus (15)

• Gravitational waves from instabilities in relativistic stars
• Perturbations of slowly rotating black holes: massive vector fields in the Kerr metric
• The rotational modes of relativistic stars: Numerical results
• Nonlinear Development of the R Mode Instability and the Maximum Rotation Rate of Neutron Stars
• Non-axisymmetric oscillations of differentially rotating relativistic stars
• Eigenmode frequency distribution of rapidly rotating neutron stars
• Temperature-dependent r-modes in superfluid neutron stars stratified by muons
• Relativistic r-modes and Shear viscosity: regularizing the continuous spectrum
• The r-modes of slowly rotating, stratified neutron stars
• On a role of corotation radius in the low $T/W$ dynamical instability of differentially rotating stars
• Nonlinear Decay of r modes in Rapidly Rotating Neutron Stars
• Formulating the r-mode problem for slowly rotating neutron stars
• Radiation driven instability of rapidly rotating relativistic stars: criterion and evolution equations via multipolar expansion of gravitational waves
• Non-analytic behavior of the relativistic r-modes in slowly rotating neutron stars
• Inertial modes in stratified rotating neutron stars : An evolutionary description