Topology of the Misner Space and its g-boundary

TL;DR

This paper analyzes the topology of the Misner space, a simplified model of Taub-NUT space, and establishes its boundary structure using the concept of g-boundaries, providing explicit topological descriptions.

Contribution

It provides an explicit topological base for the complete Misner space and links certain boundary-like regions to g-boundaries, enhancing understanding of its structure.

Findings

Explicit topology base for Misner space

Identification of boundary regions as g-boundaries

Clarification of Misner space's pathological behaviors

Abstract

The Misner space is a simplified $2$-dimensional model of the $4$-dimensional Taub-NUT space that reproduces some of its pathological behaviours. In this paper we provide an explicit base of the topology of the complete Misner space $\mathbb{R}^{1,1}/boost$. Besides we prove that some parts of this space, that behave like topological boundaries, are equivalent to the $g$-boundaries of the Misner space.