Equilibrium Configurations of Homogeneous Fluids in General Relativity

Abstract

By means of a highly accurate, multi-domain, pseudo-spectral method, we investigate the solution space of uniformly rotating, homogeneous and axisymmetric relativistic fluid bodies. It turns out that this space can be divided up into classes of solutions. In this paper, we present two new classes including relativistic core-ring and two-ring solutions. Combining our knowledge of the first four classes with post-Newtonian results and the Newtonian portion of the first ten classes, we present the qualitative behaviour of the entire relativistic solution space. The Newtonian disc limit can only be reached by going through infinitely many of the aforementioned classes. Only once this limiting process has been consummated, can one proceed again into the relativistic regime and arrive at the analytically known relativistic disc of dust.

8 pages, colour figures, v3: minor additions including one reference, accepted by MNRAS

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Cited by in corpus (7)

• On the Solution Space of Differentially Rotating Neutron Stars in General Relativity
• Uniformly Rotating Rings in General Relativity
• Post-Newtonian reference-ellipsoid for relativistic geodesy
• An approximate global solution of Einstein's equation for a rotating compact source with linear equation of state
• Uniformly Rotating Polytropic Rings in Newtonian Gravity
• Uniformly Rotating Homogeneous and Polytropic Rings in Newtonian Gravity
• The Parametric Transition of Strange Matter Rings to a Black Hole