

Recently, the dynamical evolution of rapidly rotating stars has
become possible in numerical relativity. In the framework of the
3+1 split of the Einstein equations [284], a stationary axisymmetric star can be described by a metric of
the standard form
where
is the lapse function,
is the shift three-vector, and
is the spatial three-metric, with
. The spacetime has the following properties:
- The metric function
in (5
) describing the dragging of inertial frames by rotation is
related to the shift vector through
. This shift vector satisfies the
minimal distortion shift
condition.
- The metric satisfies the
maximal slicing
condition, while the lapse function is related to the metric
function
in (5
) through
.
- The quasi-isotropic coordinates are suitable for numerical
evolution, while the radial-gauge coordinates [25
] are not suitable for nonspherical sources (see [47] for details).
- The ZAMOs are the Eulerian observers, whose worldlines are
normal to the
hypersurfaces.
- Uniformly rotating stars have
in the
coordinate frame
. This can be shown by requiring a vanishing rate of
shear.
- Normal modes of pulsation are discrete in the coordinate
frame and their frequencies can be obtained by Fourier
transforms (with respect to coordinate time
t) of evolved variables at a fixed coordinate location [106
].
Crucial ingredients for the successful long-term evolutions of
rotating stars in numerical relativity are the conformal ADM
schemes for the spacetime evolution (see [234,
277,
32,
4]) and hydrodynamical schemes that have been shown to preserve
well the sharp rotational profile at the surface of the
star [106
,
294
,
105
].


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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
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