Two-dimensional gravity with a dynamical aether

TL;DR

This paper explores the classical solutions of two-dimensional Einstein-aether gravity, revealing how solutions vary with the coupling constant and providing insights for quantum gravity models with a preferred frame.

Contribution

It presents a detailed analysis of classical solutions in 2D Einstein-aether theory, highlighting the dependence on coupling sign and characterizing solution types and their properties.

Findings

Solutions depend on the sign of the coupling constant.

Positive coupling yields flat, de Sitter, anti-de Sitter, and singular spacetimes.

Negative coupling yields flat and singular spacetimes only.

Abstract

We investigate the two-dimensional behavior of gravity coupled to a dynamical unit timelike vector field, i.e. "Einstein-aether theory". The classical solutions of this theory in two dimensions depend on one coupling constant. When this coupling is positive the only solutions are (i) flat spacetime with constant aether, (ii) de Sitter or anti-de Sitter spacetimes with a uniformly accelerated unit vector invariant under a two-dimensional subgroup of SO(2,1) generated by a boost and a null rotation, and (iii) a non-constant curvature spacetime that has no Killing symmetries and contains singularities. In this case the sign of the curvature is determined by whether the coupling is less or greater than one. When instead the coupling is negative only solutions (i) and (iii) are present. This classical study of the behavior of Einstein-aether theory in 1+1 dimensions may provide a starting point for further investigations into semiclassical and fully quantum toy models of quantum gravity with a dynamical preferred frame.