Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-11-02
Gen.Rel.Grav.39:707-736,2007
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
32 pages, no figures. Submitted to GRG
Scientific paper
10.1007/s10714-007-0414-6
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
Cabezas J. A.
Martin-Martin J.
Molina Alberto
Ruiz Eduardo
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