Through the Singularity

TL;DR

This paper explores a theoretical framework for passing through black hole singularities by generalizing the concepts of smoothness and curves in differential spaces, enabling a potential passage between universes or from black holes to white holes.

Contribution

It introduces a novel approach using ringed spaces and generalized curves to model smooth passage through singularities in spacetime.

Findings

A new mathematical framework for singularities using ringed spaces.

Smooth passage through singularities is theoretically possible with generalized curves.

Provides insights into black hole to white hole transitions.

Abstract

In this work, we propose a dangerous journey -- a journey through the strong singularity from one universe to another or from inside of a black hole to its 'inverse' as a white hole. Such singularities are hidden in the Friedman and Schwarzschild solutions; we call them malicious singularities. The journey is made possible owing to two generalizations. The first generalization consists in considering spaces with differential structures on them (the so-called ringed spaces) rather than the usual manifolds. This entails a generalization of the concept of smoothness, which allows us to think about a smooth passage through the singularity. The second generalization is related to the concept of curve. We show that if a kind of singularity is implanted in the set of curve's parameters, along with an appropriate topology, in such a way that the structure of the set of parameters corresponds to the structure of the singular space-time, the curve can smoothly -- in a generalized sense -- pass through the singularity.