Hausdorff closed limits and the c-boundary II: null infinity and black holes

Abstract

We have shown in a companion paper (e Silva et al (2019)) that when a spacetime is globally hyperbolic with a (possibly empty) smooth timelike boundary , then a metrizable topology, the closed limit topology (CLT), can be advantageously adopted on the Geroch–Kronheimer–Penrose causal completion (or c-completion for short) of . The CLT retains essentially all the good properties of other topologies previously defined in the literature, such as the well-known chronological topology. In this paper we prove that if a globally hyperbolic spacetime admits a conformal boundary, defined in such broad terms as to include all the standard examples in the literature, then the latter is homeomorphic to the causal boundary endowed with the CLT. Then, we revisit the new definitions of (future) null infinity and black hole as given in terms of the c-boundaries in another recent work Costa e Silva et al (2018 J. High Energy Phys. JHEP(2018)123). We show that a number of the attending technicalities can be simplified for globally hyperbolic spacetimes when the CLT is considered.