Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-06-27
Class.Quant.Grav. 21 (2004) 4661-4676
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
considerably revised version, to appear in Class. Quantum. Grav
Scientific paper
10.1088/0264-9381/21/19/012
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.
Andersson Nils.
Lockitch Keith H.
Watts Anna L.
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