

Pulsations of rotating relativistic stars are traditionally
studied (when possible) as a time independent, linear eigenvalue
problem, but recent advances in numerical relativity also allow
the study of such pulsations via numerical time evolutions. The
first quasi-radial mode frequencies of rapidly rotating stars in
full general relativity have been recently obtained in [105
], something that has not been achieved yet with linear
perturbation theory. The fundamental quasi-radial mode in full
general relativity has a similar rotational dependence as in the
relativistic Cowling approximation, and an empirical relation
between the full GR computation and the Cowling approximation can
be constructed (Figure
18). For higher order modes, apparent intersections of mode
sequences near the mass-shedding limit do not allow for such
empirical relations to be constructed.
In the relativistic Cowling approximation, 2D time evolutions
have yielded frequencies for the
l
=0 to
l
=3 axisymmetric modes of rapidly rotating relativistic polytropes
with
N
=1.0 [104
]. The higher order overtones of these modes show characteristic
apparent crossings near mass-shedding (as was observed for the
quasi-radial modes in [330]).
Figure 18:
The first fully relativistic, quasi-radial pulsation
frequencies for a sequence of rapidly rotating stars (solid
lines). The frequencies of the fundamental mode
F (filled squares) and of the first overtone
(filled circles) are obtained through
coupled
hydrodynamical and spacetime evolutions. The corresponding
frequencies obtained from computations in the relativistic
Cowling approximation [104] are shown as dashed lines. (Figure 16 of Font, Goodale,
Iyer, Miller, Rezzolla, Seidel, Stergioulas, Suen, and
Tobias [105].)
Numerical relativity has also enabled the first study of
nonlinear
r
-modes in rapidly rotating relativistic stars (in the Cowling
approximation) by Stergioulas and Font [294]. For several dozen dynamical timescales, the study shows that
nonlinear
r
-modes with amplitudes of order unity can exist in a star
rotating near mass-shedding. However, on longer timescales,
nonlinear effects may limit the
r
-mode amplitude to smaller values (see Section
3.5.3).


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Rotating Stars in Relativity
Nikolaos Stergioulas
http://www.livingreviews.org/lrr-2003-3
© Max-Planck-Gesellschaft. ISSN 1433-8351
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