Classical Signature Change in the Black Hole Topology

TL;DR

This paper explores how classical signature change can prevent singularities in gravitational collapse, proposing a model where black hole re-birth involves a double signature change with potential implications for universe evolution.

Contribution

It introduces a novel model of black hole re-birth via double signature change, extending classical signature change concepts from cosmology to gravitational collapse.

Findings

Signature change can avoid black hole singularities.

Realistic models require non-zero density inside horizons.

Geodesic matching implies particle mass jumps across signature surfaces.

Abstract

Investigations of classical signature change have generally envisaged applications to cosmological models, usually a Friedmann-Lemaitre-Robertson-Walker model. The purpose has been to avoid the inevitable singularity of models with purely Lorentzian signature, replacing the neighbourhood of the big bang with an initial, singularity free region of Euclidean signture, and a signature change. We here show that signature change can also avoid the singularity of gravitational collapse. We investigate the process of re-birth of Schwarzschild type black holes, modelling it as a double signature change, joining two universes of Lorentzian signature through a Euclidean region which provides a `bounce'. We show that this process is viable both with and without matter present, but realistic models -- which have the signature change surfaces hidden inside the horizons -- require non-zero density. In fact the most realistic models are those that start as a finite cloud of collapsing matter, surrounded by vacuum. We consider how geodesics may be matched across a signature change surface, and conclude that the particle `masses' must jump in value. This scenario may be relevant to Smolin's recent proposal that a form of natural selection operates on the level of universes, which favours the type of universe we live in.