Causality in 3D Massive Gravity Theories

TL;DR

This paper investigates the causality constraints in various 2+1 dimensional massive gravity theories, revealing conditions under which causality and unitarity coexist and highlighting differences from higher-dimensional theories.

Contribution

It provides a detailed analysis of causality and unitarity in 2+1D massive gravity theories, including extensions like Born-Infeld and minimal massive gravity, contrasting with higher-dimensional cases.

Findings

Causality and unitarity are compatible in certain 2+1D theories with negative Newton's constant.

Extensions like Born-Infeld gravity show similar causality-unitarity relations as their lower-dimensional counterparts.

Higher-dimensional quadratic and cubic theories exhibit conflicts between causality and unitarity.

Abstract

We study the constraints coming from local causality requirement in various $2+1$ dimensional dynamical theories of gravity. In topologically massive gravity, with a single parity non-invariant massive degree of freedom, and in new massive gravity, with two massive spin-$2$ degrees of freedom, causality and unitarity are compatible with each other and both require the Newton's constant to be negative. In their extensions, such as the Born-Infeld gravity and the minimal massive gravity the situation is similar and quite different from their higher dimensional counterparts, such as quadratic (e.g., Einstein-Gauss-Bonnet) or cubic theories, where causality and unitarity are in conflict. We study the problem both in asymptotically flat and asymptotically anti-de Sitter spaces.