Regularizing the r-mode problem for non-barotropic relativistic stars

Lockitch, Keith H., Andersson, Nils and Watts, Anna L. (2004) Regularizing the r-mode problem for non-barotropic relativistic stars. Classical and Quantum Gravity, 21 (19), 4661-4675. (doi:10.1088/0264-9381/21/19/012).

Record type: Article

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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