3.1 Quasi-normal modes of oscillationRotating Stars in Relativity2.10 Rotating relativistic stars in

3 Oscillations and Stability

The study of oscillations of relativistic stars is motivated by the prospect of detecting such oscillations in electromagnetic or gravitational wave signals. In the same way that helioseismology is providing us with information about the interior of the Sun, the observational identification of oscillation frequencies of relativistic stars could constrain the high-density equation of state [13]. The oscillations could be excited after a core collapse or during the final stages of a neutron star binary merger. Rapidly rotating relativistic stars can become unstable to the emission of gravitational waves.

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, 118Jump To The Next Citation Point In The Article], but the Eulerian approach proved to be more suitable for numerical computations of mode frequencies and eigenfunctions [162Jump To The Next Citation Point In The Article, 218Jump To The Next Citation Point In The Article, 158Jump To The Next Citation Point In The Article, 160Jump To The Next Citation Point In The Article, 159Jump To The Next Citation Point In The Article]. 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.  [156Jump To The Next Citation Point In The Article] and in the Eulerian approach by Managan [218Jump To The Next Citation Point In The Article] and Ipser and Lindblom [158Jump To The Next Citation Point In The Article]. While a lot has been learned from Newtonian studies, in the following we will focus on the relativistic treatment of oscillations of rotating stars.





3.1 Quasi-normal modes of oscillationRotating Stars in Relativity2.10 Rotating relativistic stars in

image Rotating Stars in Relativity
Nikolaos Stergioulas
http://www.livingreviews.org/lrr-2003-3
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