Topology of the ambient boundary and the convergence of causal curves

Abstract

We discuss the topological nature of the boundary spacetime, the conformal infinity of the ambient cosmological metric. Due to the existence of a homothetic group, the bounding spacetime must be equipped not with the usual Euclidean metric topology but with the Zeeman fine topology. This then places severe constraints to the convergence of a sequence of causal curves and the extraction of a limit curve, and also to our ability to formulate conditions for singularity formation.

8 pages

References in corpus (1)

• Production of $\Sigma (1385{)}^{\pm }$ and $\Xi (1530{)}^0$ in proton-proton collisions at $\sqrt{s}=$ 7 TeV

Cited by in corpus (8)

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• On the Possibility of Singularities on the Ambient Boundary
• Natural vs. Artificial Topologies on a Relativistic Spacetime
• On the Causal and Topological Structure of the $2$-Dimensional Minkowski Space
• Spacetimes as topological spaces, and the need to take methods of general topology more seriously
• Are four dimensions enough, a note on ambient cosmology