2009/04/30 by A. Di Prisco, A. di Prisco, L. Herrera +2 · 72 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Boundary (topology) #Boundary value problem #Classical mechanics #Cosmology and Gravitation Theories #Diagonal #Einstein #General relativity #Geometry #Gravitation #Gravitational collapse #Isotropy #Mathematical analysis #Mathematical physics #Mathematics #Metric (unit) #Perfect fluid #Physics #Quantum mechanics #Spacetime #Theoretical physics #gr-qc
paper · pdf · doi:10.1103/physrevd.80.064031
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 80(6) (American Physical Society) · RevTeX. References added, and discussion amended and extended in response to referee reports. Accepted for publication in Phys. Rev. D
arxiv created 2009/08/14 · openalex publication_date 2009/09/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider diagonal cylindrically symmetric metrics, with an interior representing a general nonrotating 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 nonstatic 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, Chrusciel, and Moncrief. 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.