Are four dimensions enough, a note on ambient cosmology
arXiv:1901.01843 · doi:10.1142/S0219887819500907
Abstract
The group of homothetic symmetries in the conformal infinity (the -dimensional "ambient boundary") of a -dimensional spacetime restricts the choice of topology to a topology under which the group of homeomorphisms of a spacetime manifold is the group of homothetic transformations. Since there are such spacetime topologies in the class of Zeeman-Göbel, under which the formation of basic contradiction present in proofs of singularity theorems is impossible, an important question is raised: why should one construct a -dimensional metric, in order to return back such a topology to its -dimensional conformal boundary, while such topologies, like those ones in the Zeeman-Göbel class, are already considered as more "natural" topologies for a spacetime, rather than the artificial (according to Zeeman) manifold topology?