Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2003-11-30
Class.Quant.Grav. 21 (2004) 3845-3870
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
new version - corrected boundary surface discussion, improved presentation, and corrected reference 22 pages, many figures
Scientific paper
10.1088/0264-9381/21/16/002
We investigate timelike junctions (with surface layer) between spherically symmetric solutions of the Einstein-field equation. In contrast to previous investigations this is done in a coordinate system in which the junction surface motion is absorbed in the metric, while all coordinates are continuous at the junction surface. The evolution equations for all relevant quantities are derived. We discuss the no-surface layer case (boundary surface) and study the behaviour for small surface energies. It is shown that one should expect cases in which the speed of light is reached within a finite proper time. We carefully discuss necessary and sufficient conditions for a possible matching of spherically symmetric sections. For timelike junctions between spherically symmetric space-time sections we show explicitly that the time component of the Lanczos equation always reduces to an identity (independently of the surface equation of state). The results are applied to the matching of FLRW models. We discuss `vacuum bubbles' and closed-open junctions in detail. As illustrations several numerical integration results are presented, some of them indicate that the junction surface can reach the speed of light within a finite time.
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