When the oscillations of an equilibrium star are of small magnitude compared to its radius, it will suffice to approximate them as linear perturbations. Such perturbations can be described in two equivalent ways. In the Lagrangian approach, one studies the changes in a given fluid element as it oscillates about its equilibrium position. In the Eulerian approach, one studies the change in fluid variables at a fixed point in space. Both approaches have their strengths and weaknesses.
In the Newtonian limit, the Lagrangian approach has been used
to develop variational principles [216,
118], but the Eulerian approach proved to be more suitable for
numerical computations of mode frequencies and
eigenfunctions [162
,
218
,
158
,
160
,
159
]. Clement [64] used the Lagrangian approach to obtain axisymmetric normal
modes of rotating stars, while nonaxisymmetric solutions were
obtained in the Lagrangian approach by Imamura
et al.
[156
] and in the Eulerian approach by Managan [218
] and Ipser and Lindblom [158
]. While a lot has been learned from Newtonian studies, in the
following we will focus on the relativistic treatment of
oscillations of rotating stars.
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Rotating Stars in Relativity
Nikolaos Stergioulas http://www.livingreviews.org/lrr-2003-3 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei.mpg.de |