2.4 Equations of structure2 The Equilibrium Structure of 2.2 Geometry of spacetime

2.3 The rotating fluid

When sources of non-isotropic stresses (such as a magnetic field or a solid state of parts of the star), viscous stresses, and heat transport are neglected in constructing an equilibrium model of a relativistic star, then the matter can be modeled as a perfect fluid, described by the stress-energy tensor

equation122

where tex2html_wrap_inline3808 is the fluid's 4-velocity. In terms of the two Killing vectors tex2html_wrap_inline3724 and tex2html_wrap_inline3726, the 4-velocity can be written as

equation126

where v is the 3-velocity of the fluid with respect to a local ZAMO, given by

equation130

and tex2html_wrap_inline3816 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 (tex2html_wrap_inline3818 const.) is a special case (see Section  2.5).



2.4 Equations of structure2 The Equilibrium Structure of 2.2 Geometry of spacetime

image Rotating Stars in Relativity
Nikolaos Stergioulas
http://www.livingreviews.org/lrr-2003-3
© Max-Planck-Gesellschaft. ISSN 1433-8351
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