The Causal Structure of Two-Dimensional Spacetimes

TL;DR

This paper explores the causal structure of two-dimensional spacetimes, demonstrating local solution flexibility, examining black hole smoothness effects, and discussing the applicability of classical singularity theorems in 2D.

Contribution

It shows that any 2D spacetime can be locally realized with suitable matter fields and analyzes how black hole properties differ from higher dimensions.

Findings

Any 2D spacetime is locally a solution with appropriate matter fields.

In 2D, black hole size cannot increase if an area theorem analogue holds.

Classical singularity theorems have limited applicability in 2D.

Abstract

We investigate the causal structure of $(1+1)$-dimensional spacetimes. For two sets of field equations we show that at least locally any spacetime is a solution for an appropriate choice of the matter fields. For the theories under consideration we investigate how smoothness of their black hole solutions affects time orientation. We show that if an analog to Hawking's area theorem holds in two spacetime dimensions, it must actually state that the size of a black hole never {\em increases}, contrary to what happens in four dimensions. Finally, we discuss the applicability of the Penrose and Hawking singularity theorems to two spacetime dimensions.