A Global View of Kinks in 1+1 Gravity

TL;DR

This paper explores the structure and extensions of kink solutions in 1+1 dimensional gravity, revealing new geometric insights and constructing families of inequivalent kinks with implications for various gravity models.

Contribution

It constructs maximal extensions of kink spacetimes, generalizes known examples, and demonstrates the existence of continuous families of inequivalent kinks in 2D gravity.

Findings

Maximal extensions of kink spacetimes are constructed using Penrose diagrams.

Continuous one-parameter families of inequivalent kinks exist in 2D gravity.

Results apply to flat, de Sitter, and generalized dilaton gravity solutions.

Abstract

Following Finkelstein and Misner, kinks are non-trivial field configurations of a field theory, and different kink-numbers correspond to different disconnected components of the space of allowed field configurations for a given topology of the base manifold. In a theory of gravity, non-vanishing kink-numbers are associated to a twisted causal structure. In two dimensions this means, more specifically, that the light-cone tilts around (non-trivially) when going along a non-contractible non-selfintersecting loop on spacetime. One purpose of this paper is to construct the maximal extensions of kink spacetimes using Penrose diagrams. This will yield surprising insights into their geometry but also allow us to give generalizations of some well-known examples like the bare kink and the Misner torus. However, even for an arbitrary 2D metric with a Killing field we can construct continuous one-parameter families of inequivalent kinks. This result has already interesting implications in the flat or deSitter case, but it applies e.g. also to generalized dilaton gravity solutions. Finally, several coordinate systems for these newly obtained kinks are discussed.