Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-04-04
Phys.Rev.D80:064031,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
RevTeX. References added, and discussion amended and extended in response to referee reports. Accepted for publication in Phys
Scientific paper
10.1103/PhysRevD.80.064031
We consider diagonal cylindrically symmetric metrics, with an interior representing a general non-rotating fluid with anisotropic pressures. An exterior vacuum Einstein-Rosen spacetime is matched to this using Darmois matching conditions. We show that the matching conditions can be explicitly solved for the boundary values of metric components and their derivatives, either for the interior or exterior. Specializing to shearfree interiors, a static exterior can only be matched to a static interior, and the evolution in the non-static case is found to be given in general by an elliptic function of time. For a collapsing shearfree isotropic fluid, only a Robertson-Walker dust interior is possible, and we show that all such cases were included in Cocke's discussion. For these metrics, Nolan and Nolan have shown that the matching breaks down before collapse is complete and Tod and Mena have shown that the spacetime is not asymptotically flat in the sense of Berger et al. The issues about energy that then arise are revisited and it is shown that the exterior is not in an intrinsic gravitational or superenergy radiative state at the boundary.
Herrera Luis
MacCallum Malcolm A. H.
Prisco A. Di
Santos Nilton O.
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