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.

arXiv comment34 pages: second half of the original arXiv:2005.11324 (now shortened)

References in corpus (21)

• The Pre-Big Bang Scenario in String Cosmology
• Classical Black Hole Production in High-Energy Collisions
• Loop quantum cosmology of Bianchi I models
• Loop Quantum Cosmology: An Overview
• Resolving Cosmological Singularities
• Black holes from high-energy beam--beam collisions
• Pre-big bang bubbles from the gravitational instability of generic string vacua
• Quantum gravitational Kasner transitions in Bianchi-I spacetime
• The loop quantum cosmology bounce as a Kasner transition
• A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on T3
• Regular two-component bouncing cosmologies and perturbations therein
• The characteristic initial value problem for plane symmetric spacetimes with weak regularity
• On the geometry of impulsive gravitational waves
• The causal boundary of wave-type spacetimes
• Initial Conditions and the Structure of the Singularity in Pre-Big-Bang Cosmology
• O(d,d)-invariant collapse/inflation from colliding superstring waves
• A generalized Kasner transition for bouncing Bianchi I models in modified gravity theories
• Compensated compactness and corrector stress tensor for the Einstein equations in T2 symmetry
• On the global evolution of self-gravitating matter. Nonlinear interactions in Gowdy symmetry
• Universal scattering laws for quiescent bouncing cosmology
• Cyclic spacetimes through singularity scattering maps. The laws of quiescent bounces