2.3 Equations of State2 The Equilibrium Structure of 2.1 Assumptions

2.2 Geometry of Space-Time

In relativity, the space-time geometry of a rotating star in equilibrium is described by a stationary and axisymmetric metric of the form

  equation34

where tex2html_wrap_inline1975, tex2html_wrap_inline1977, tex2html_wrap_inline1979 and tex2html_wrap_inline1981 are four metric functions which depend on the coordinates r and tex2html_wrap_inline1985 only (unless otherwise noted, we assume c = G =1). The perfect fluid has a stress-energy tensor

equation40

a four velocity

equation44

and a 3-velocity with respect to a zero angular momentum observer of

equation48

where tex2html_wrap_inline1989 and tex2html_wrap_inline1991 are the two killing vectors associated with the time and translational symmetries of the space-time, tex2html_wrap_inline1993 is the metric tensor, and tex2html_wrap_inline1995 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

equation52

(where tex2html_wrap_inline1997 is the Ricci tensor and tex2html_wrap_inline1999) and the equation of hydrostationary equilibrium.



2.3 Equations of State2 The Equilibrium Structure of 2.1 Assumptions

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