In a continuous sequence of rotating stars, a quasinormal mode
of index
l
is defined as the mode which, in the nonrotating limit, reduces
to the quasinormal mode of the same index
l
. Rotation has several effects on the modes of a previously
nonrotating star:
 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.
 Prograde (m
<0) modes are now different than retrograde (m
>0) modes.
 A rotating ``polar''
l
mode consists of a sum of purely polar and purely axial terms
[42]
that is, rotation couples a polar
l
term to an axial
term (the coupling to the
l
+1 term is, however, strongly favored over the coupling to the
l
1 term [91]). Similarly, for a rotating ``axial'' mode,
 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, quasinormal modes of oscillation have only
been studied in the slowrotation limit, in the postNewtonian
and in the Cowling Approximations. The solution of the
fullyrelativistic 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 [42,
92].

Going further.
The equations that describe oscillations of the solid crust of
a rapidly rotating relativistic star are derived by Priou in [93]. The effects of superfluid hydrodynamics on the oscillations
of neutron stars are investigated by Lindblom and Mendell in [94].

Rotating Stars in Relativity
Nikolaos Stergioulas
http://www.livingreviews.org/lrr19988
© MaxPlanckGesellschaft. ISSN 14338351
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livrev@aeipotsdam.mpg.de
