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

Regularizing the r-mode problem for non-barotropic relativistic stars
Regularizing the r-mode problem for non-barotropic relativistic stars
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.
0264-9381
4661-4675
Lockitch, Keith H.
e5c44256-3ae5-42e8-989b-f5d07683c3ba
Andersson, Nils
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Watts, Anna L.
8c906b14-9fb9-4f04-9cb3-2aabd6561162
Lockitch, Keith H.
e5c44256-3ae5-42e8-989b-f5d07683c3ba
Andersson, Nils
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Watts, Anna L.
8c906b14-9fb9-4f04-9cb3-2aabd6561162

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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Published date: 2004

Identifiers

Local EPrints ID: 40767
URI: http://eprints.soton.ac.uk/id/eprint/40767
ISSN: 0264-9381
PURE UUID: 1216853f-2ad7-4261-8f51-e4893a44c8ec
ORCID for Nils Andersson: ORCID iD orcid.org/0000-0001-8550-3843

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Date deposited: 07 Jul 2006
Last modified: 09 Jan 2022 02:57

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Contributors

Author: Keith H. Lockitch
Author: Nils Andersson ORCID iD
Author: Anna L. Watts

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