Spacetimes Coverings and C-Boundary

TL;DR

This paper explores the relationship between the c-completion of Lorentz manifolds and their quotients under isometry groups, providing conditions for when these structures are well-behaved and establishing homeomorphisms between their completions.

Contribution

It characterizes when the c-completion of a Lorentz manifold and its quotient are topologically and causally equivalent, extending previous results and applying to Robertson-Walker spacetimes.

Findings

Established conditions for well-behaved quotients with the future chronological topology

Proved existence of homeomorphism and chronological isomorphism between c-completions of V and M

Applied results to Robertson-Walker spacetimes, including Anti-de Sitter models

Abstract

We consider the relation between the c-completion of a Lorentz manifold V and its quotient M = V/G, where G is an isometry group acting freely and properly discontinuously. First, we consider the future causal completion case, characterizing virtually when such a quotient is well behaved with the future chronological topology and improving the existing results on the literature. Secondly, we show that under some general assumptions, there exists an homeomorphism and chronological isomorphism between both, the c-completion of M and some adequate quotient of the c-completion of V defined by G. Our results are optimal, as we show in several examples. Finally, we give a practical application by considering isometric actions over Robertson-Walker spacetimes, including in particular the Anti-de Sitter model.