2019/09/09 by Müller, Olaf · 1 citation
#53C50 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1909.03797
On the Geroch-Kronheimer-Penrose future completion IP(X) of a spacetime X, there are two frequently used topologies. We systematically examine τ+, the stronger (metrizable) of them, which is the coarsest causally continuous topology, obtaining a variety of novel results, among them a complete characterization of the difference in convergence between both topologies. In our framework, we can allow for X being a chr. space and consequently for the interpretation of IP as an idempotent functor on a category that includes spacetimes of very low regularity. Furthermore, we explicitly calculate (IP(X), τ+) for multiply warped chronological spaces.