Second-order hyperbolic Fuchsian systems: Asymptotic behavior of geodesics in Gowdy spacetimes

Journal Article · Sat Oct 15 00:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.84.084036· OSTI ID:21607919

Beyer, Florian; LeFloch, Philippe G ^[1]

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1. Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin 9054 (New Zealand)

Recent work by the authors led to the development of a mathematical theory dealing with 'second-order hyperbolic Fuchsian systems', as we call them. In the present paper, we adopt a physical standpoint and discuss the implications of this theory which provides one with a new tool to tackle the Einstein equations of general relativity (under certain symmetry assumptions). Specifically, we formulate the 'Fuchsian singular initial value problem' and apply our general analysis to the broad class of vacuum Gowdy spacetimes with spatial toroidal topology. Our main focus is on providing a detailed description of the asymptotic geometry near the initial singularity of these inhomogeneous cosmological spacetimes and, especially, analyzing the asymptotic behavior of timelike geodesics - which represent the trajectories of freely falling observers - and null geodesics. In particular, we numerically construct Gowdy spacetimes which contain a black hole-like region together with a flat Minkowski-like region. By using the Fuchsian technique, we investigate the effect of the gravitational interaction between these two regions and we study the unexpected behavior of geodesic trajectories within the intermediate part of the spacetime limited by these two regions.

• OSTI ID: 21607919
• Journal Information: Physical Review. D, Particles Fields, Vol. 84, Issue 8; Other Information: DOI: 10.1103/PhysRevD.84.084036; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
79 ASTROPHYSICS
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GENERAL RELATIVITY THEORY
GEODESICS
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