3.3 Axisymmetric Perturbation3 Oscillations and Stability3.1 Quasi-Normal Modes of Oscillation

3.2 Effect of Rotation on Quasi-Normal Modes

In a continuous sequence of rotating stars, a quasi-normal mode of index l is defined as the mode which, in the nonrotating limit, reduces to the quasi-normal mode of the same index l . Rotation has several effects on the modes of a previously nonrotating star:
  1. The degeneracy in the index m is removed and a nonrotating mode of index l is split into 2 l +1 different (l, m) modes.
  2. Prograde (m <0) modes are now different than retrograde (m >0) modes.
  3. A rotating ``polar'' l -mode consists of a sum of purely polar and purely axial terms [42Jump To The Next Citation Point In The Article]

    equation332

    that is, rotation couples a polar l -term to an axial tex2html_wrap_inline2275 term (the coupling to the l +1 term is, however, strongly favored over the coupling to the l -1 term [91Jump To The Next Citation Point In The Article]). Similarly, for a rotating ``axial'' mode,

    equation339

  4. Frequencies and damping times are shifted. In general, frequencies (in the inertial frame) of prograde modes increase, while those of retrograde modes decrease with increasing rate of rotation.

In rotating stars, quasi-normal modes of oscillation have only been studied in the slow-rotation limit, in the post-Newtonian and in the Cowling Approximations. The solution of the fully-relativistic perturbation equations for a rapidly rotating star is still a very challenging task, and only recently have they been solved for zero- frequency (neutral) modes [42Jump To The Next Citation Point In The Article, 92Jump To The Next Citation Point In The Article].



3.3 Axisymmetric Perturbation3 Oscillations and Stability3.1 Quasi-Normal Modes of Oscillation

image Rotating Stars in Relativity
Nikolaos Stergioulas
http://www.livingreviews.org/lrr-1998-8
© Max-Planck-Gesellschaft. ISSN 1433-8351
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