The causal boundary of wave-type spacetimes

Abstract

A complete and systematic approach to compute the causal boundary of wave-type spacetimes is carried out. The case of a 1-dimensional boundary is specially analyzed and its critical appearance in pp-wave type spacetimes is emphasized. In particular, the corresponding results obtained in the framework of the AdS/CFT correspondence for holography on the boundary, are reinterpreted and very widely generalized. Technically, a recent new definition of causal boundary is used and stressed. Moreover, a set of mathematical tools is introduced (analytical functional approach, Sturm-Liouville theory, Fermat-type arrival time, Busemann-type functions).

41 pages, 1 table. Included 4 new figures, and some small modifications. To appear in JHEP

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• The geometry of modified Riemannian extensions
• Wind Finslerian structures: from Zermelo's navigation to the causality of spacetimes
• Penrose's 1965 singularity theorem: From geodesic incompleteness to cosmic censorship
• The causal boundary of product spacetimes
• Completeness of the Trajectories of Particles Coupled to a General Force Field
• Causal boundaries and holography on wave type spacetimes
• Isocausal spacetimes may have different causal boundaries
• Ehlers-Kundt Conjecture about Gravitational Waves and Dynamical Systems
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• Remarks on the completeness of trajectories of accelerated particles in Riemannian manifolds and plane waves
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• Hausdorff closed limits and the causal boundary of globally hyperbolic spacetimes with timelike boundary
• Cyclic spacetimes through singularity scattering maps. Plane-symmetric gravitational collisions
• Spacetimes Coverings and C-Boundary