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.

Rotating Stars in Relativity
Nikolaos Stergioulas
http://www.livingreviews.org/lrr-1998-8
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