# Taming Dirac strings and timelike loops in vacuum gravity

## TL;DR

This paper introduces a method to remove singularities like Dirac strings and closed timelike curves in vacuum gravity solutions, providing smooth, extended geometries with a geometric interpretation of magnetic charge.

## Contribution

It presents a novel approach to eliminate singularities in classical gravity solutions, extending the Taub-NUT and Misner geometries into smooth, degenerate metric phases.

## Key findings

- Elimination of Dirac string singularities in Taub-NUT geometry.
- Smooth extension of Misner geometry without closed timelike curves.
- Provides a geometric interpretation of magnetic charge in gravity.

## Abstract

The problem of singularities associated with Dirac strings and closed timelike curves in classical solutions of pure gravity is analyzed here. A method to eliminate these is introduced and established first for the Taub-NUT geometry. This is superceded by a smooth solution of first order field equations, which is defined to be a unique extension of the Taub Universe to a degenerate metric phase. As an additional feature, this framework naturally provides a geometric interpretation of the magnetic charge in the context of gravity theory without matter. Finally, exploiting the two phases of the metric determinant, we find a (smooth and unique) continuation of the Misner geometry as well, ridding it of closed timelike worldlines which exist in its otherwise Einsteinian manifestation.