# Exotic Massive Gravity: Causality and a Birkhoff-like Theorem

## TL;DR

This paper investigates causality in exotic massive gravity in three dimensions, demonstrating time-delay behavior and establishing a Birkhoff-like theorem with exact solutions, contributing to understanding of the theory's properties.

## Contribution

It provides the first causality analysis via time-delay computations and proves a Birkhoff-like theorem in exotic massive gravity, including new exact solutions.

## Key findings

- Time-delay observed despite ghost presence at linear level
- Any hypersurface orthogonal non-null Killing vector field leads to conformally flat solutions
- Derived new exact solutions in the theory

## Abstract

We study the local causality issue via the Shapiro time-delay computations in the on-shell consistent exotic massive gravity in three dimensions. The theory shows time-delay as opposed to time-advance despite having a ghost at the linearized level both for asymptotically flat and anti-de Sitter spacetimes. We also prove a Birkhoff-like theorem: any solution with a hypersurface orthogonal non-null Killing vector field is conformally flat; and find some exact solutions.