Causal boundaries and holography on wave type spacetimes

TL;DR

This paper reviews the concept of causal boundaries in spacetimes, especially in wave-type geometries, and explores their role in holography and the AdS/CFT correspondence, aiming to clarify the current understanding and proposals.

Contribution

It provides a comprehensive review of classical and modern approaches to causal boundaries, emphasizing their relevance in holography and proposing a clearer understanding of the c-boundary in wave spacetimes.

Findings

Revised definitions of the c-boundary improve understanding of spacetime limits.

The c-boundary plays a crucial role in holography for wave spacetimes.

Current proposals aim to resolve controversies surrounding the causal boundary concept.

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.