Black holes as portals to an Euclidean realm

Abstract

Motivated by a one-cycle cosmological scenario where the big bang marks the egress from a Euclidean metric signature regime, we investigate the possibility of black holes (BH) hosting the mirroring entryways. Analogous to the inflationary stage following the exit end, the entry portals must be enveloped by de Sitter cores inside BHs, in order to satisfy regularity conditions at the metric signature transition boundary. We examine the interior structure of BHs that could be consistent with such a physical picture, and conclude that the presence of a spacelike shell of non-inflationary matter is likely required.

Figures (1)

• Figure 1: The Penrose conformal diagram for the stitched signature change BH. Note the past singularity will be replaced by stellar interior in realistic astrophysical settings. The Euclidean region rests beyond $\Sigma$ but since it doesn't have a causal structure, we don't plot it on the Penrose diagram. Each point on this diagrams is a $S^2$ shell and the dynamical system trajectory of Sec. \ref{['sec:Dyn']} below can be seen as a spacelike path turning into a timelike one at the event horizon (hereafter abbreviated to EH), which specifies the metric and scalar field values at the spherical shells that it passes through.