where
,
,
and
are four metric functions which depend on the coordinates
r
and
only (unless otherwise noted, we assume
c
=
G
=1). The perfect fluid has a stress-energy tensor
a four velocity
and a 3-velocity with respect to a zero angular momentum observer of
where
and
are the two killing vectors associated with the time and
translational symmetries of the space-time,
is the metric tensor, and
is the angular velocity. Having specified an equation of state
for very dense matter, the structure of the star is computed by
solving four components of Einstein's gravitational field
equations
(where
is the Ricci tensor and
) and the equation of hydrostationary equilibrium.
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Rotating Stars in Relativity
Nikolaos Stergioulas http://www.livingreviews.org/lrr-1998-8 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |