An approximate global solution of Einstein's equations for a finite body

Abstract

We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using the post-Minkowskian formalism (weak-field approximation) and considering rotation as a perturbation (slow-rotation approximation), we find approximate interior and exterior (asymptotically flat) solutions to this problem in harmonic and quo-harmonic coordinates. In both cases, interior and exterior solutions are matched, in the sense of Lichnerowicz, on the surface of zero pressure to obtain a global solution. The resulting metric depends on three arbitrary constants: mass density, rotational velocity and the star radius at the non-rotation limit. The mass, angular momentum, quadrupole moment and other constants of the exterior metric are determined by these three parameters. It is easy to show that this type of fluid cannot be a source of the Kerr metric

32 pages, no figures. Submitted to GRG

References in corpus (7)

• Rotating Stars in Relativity
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• The Wahlquist metric cannot describe an isolated rotating body
• Stationary and Axisymmetric Perfect-Fluid Solutions with Conformal Motion
• Comparing metrics at large: harmonic vs quo-harmonic coordinates
• Influence of general convective motions on the exterior of isolated rotating bodies in equilibrium
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Cited by in corpus (13)

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• Slowly rotating homogeneous masses revisited
• The quadrupole moment of slowly rotating fluid balls
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• Can rigidly rotating polytropes be sources of the Kerr metric?
• Faithful transformation of quasi-isotropic to Weyl-Papapetrou coordinates: A prerequisite to compare metrics
• Source integrals of multipole moments for static space-times
• Existence and uniqueness of compact rotating configurations in GR in second order perturbation theory
• Wahlquist's metric versus an approximate solution with the same equation of state
• An approximate global solution of Einstein's equations for differentially rotating compact body
• An approximate global solution of Einstein's equations for a rotating two layers star
• Perturbation theory and harmonic gauge propagation in general relativity, a particular example