where
is the fluid's 4-velocity. In terms of the two Killing vectors
and
, the 4-velocity can be written as
where v is the 3-velocity of the fluid with respect to a local ZAMO, given by
and
is the angular velocity of the fluid in the
coordinate frame, which is equivalent to the angular velocity of the fluid as
seen by an observer at rest at infinity. Stationary
configurations can be differentially rotating, while uniform
rotation (
const.) is a special case (see Section
2.5).
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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 |