Cyclic spacetimes through singularity scattering maps. Plane-symmetric gravitational collisions

Abstract

We study the plane-symmetric collision of two gravitational waves and describe the global spacetime geometry generated by this collision. To this end, we formulate the characteristic initial value problem for the Einstein equations, when Goursat data describing the incoming waves are prescribed on two null hypersurfaces. We then construct a global solution representing a cyclic spacetime based on junction conditions associated with a prescribed singularity scattering map (a notion recently introduced by the authors). From a mathematical analysis standpoint, this amounts to a detailed analysis of the Goursat and Fuchsian initial value problems associated with singular hyperbolic equations, when junction conditions at interfaces are prescribed. In our construction, we introduce a partition into monotonicity diamonds (that is, suitable spacetime domains) and we construct the solution by concatenating domains across interfaces of timelike, null, or spacelike type.

34 pages: second half of the original arXiv:2005.11324 (now shortened)

References in corpus (7)

• Loop Quantum Cosmology: An Overview
• Quantum gravitational Kasner transitions in Bianchi-I spacetime
• The characteristic initial value problem for plane symmetric spacetimes with weak regularity
• The causal boundary of wave-type spacetimes
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• Cyclic spacetimes through singularity scattering maps. The laws of quiescent bounces