Topology of the ambient boundary and the convergence of causal curves

Antoniadis, Ignatios; Cotsakis, Spiros (2015). Topology of the ambient boundary and the convergence of causal curves. Modern Physics Letters A, 30(30), p. 1550161. World Scientific Publishing 10.1142/S0217732315501618

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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.

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