Causal boundaries and holography on wave type spacetimes

Abstract

The notion of a causal boundary for a spacetime has been a controversial topic during the last three decades. Moreover, recently the role of the boundary in the AdS/CFT correspondence for plane waves, have stimulated its redefinition with some possible alternatives. Our aim is threefold. First, to review the different classical approaches to boundaries of spacetimes, emphasizing their drawbacks and the progressive redefinitions of the c-boundary. Second, to explain how plane waves and AdS/CFT correspondence come into play, stressing the role of the c-boundary as the holographic boundary in this correspondence. And, third, to discuss the present-day status of the c-boundary, making clear the arguments of a definitive proposal.

Minor corrections and improvements in some figures. To appear un Nonlinear Analysis (2009) 35 pages, including 10 figures and one table; Latex

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• A Correspondence Between Distances and Embeddings for Manifolds: New Techniques for Applications of the Abstract Boundary
• Geometrical Approximation to the AdS/CFT Correspondence