Unboundable Spacetimes with Metric Singularities and Matching Metrics and Geodesics: A Black-White Hole and a Big Crunch-Bang

TL;DR

This paper proposes a novel approach to include metric singularities within spacetime by matching metrics and geodesics at singularities, applied to models like black-white holes and big crunch-bang scenarios.

Contribution

It introduces the concept of unboundable spacetimes with interior singularities and develops a method to match metrics and geodesics across these singularities.

Findings

Successful matching of geodesics at singularities

Application to black-white hole models

Application to big crunch-bang scenarios

Abstract

Singularity theorems of general relativity utilize the notion of causal geodesic incompleteness as a criterion of the presence of a spacetime singularity. The incompleteness of a causal curve implies the end and/or beginning of the existence of a particle, which is an event. In the commonly accepted approach, singularities are not incorporated into spacetime. Thus spacetime turns out to be event-incomplete. With creation from nothing, singularities are sources of lawlessness. A straightforward way around those conceptual problems consists in including metric singularities in spacetime and then matching metrics and causal geodesics at the singularities. To this end, a spacetime manifold is assumed to be unboundable, so that singularities may only be interior. The matching the geodesics is achieved through weakening conditions for their smoothness. This approach is applied to a black-white hole and a big crunch-bang.