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An approximate global solution of Einstein’s equation for a rotating compact source with linear equation of state. (English) Zbl 1271.83027
Gen. Relativ. Gravitation 45, No. 7, 1433-1456 (2013); erratum ibid. 45, No. 7, 1457 (2013).
Summary: We use analytic perturbation theory to present a new approximate metric for a rigidly rotating perfect fluid source with equation of state (EOS) \(\epsilon +(1-n)p = \epsilon _0\). This EOS includes the interesting cases of strange matter, constant density and the fluid of the Wahlquist metric. It is fully matched to its approximate asymptotically flat exterior using Lichnerowicz junction conditions and it is shown to be a totally general matching using Darmois-Israel conditions and properties of the harmonic coordinates. Then we analyse the Petrov type of the interior metric and show first that, in accordance with previous results, in the case corresponding to Wahlquist’s metric it can not be matched to the asymptotically flat exterior. Next, that this kind of interior can only be of Petrov types I, D or (in the static case) O and also that the non-static constant density case can only be of type I. Finally, we check that it can not be a source of Kerr’s metric.

83C25 Approximation procedures, weak fields in general relativity and gravitational theory
83C15 Exact solutions to problems in general relativity and gravitational theory
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
85A15 Galactic and stellar structure
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
Full Text: DOI
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