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Regularizing the r-mode problem for nonbarotropic relativistic stars

K. H. Lockitch·N. Andersson·A. L. Watts
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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.

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K. H. Lockitch, N. Andersson, A. L. Watts. 2004-09-10. Regularizing the r-mode problem for nonbarotropic relativistic stars. https://doi.org/10.1088/0264-9381%2F21%2F19%2F012

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