Lorentz symmetry in ghost-free massive gravity

TL;DR

This paper explores how Lorentz symmetry influences ghost-free massive gravity, analyzing solutions, stability, and gravitational wave properties, including deviations from Minkowski spacetime and their physical implications.

Contribution

It provides a comprehensive analysis of Lorentz symmetry breaking, stability of extrema, and gravitational wave polarization effects in ghost-free massive gravity.

Findings

Existence of Lorentz-invariant and breaking solutions.

Stable extrema under certain parameters.

Pentarefringence and superluminal modes in gravitational waves.

Abstract

The role of Lorentz symmetry in ghost-free massive gravity is studied, emphasizing features emerging in approximately Minkowski spacetime. The static extrema and saddle points of the potential are determined and their Lorentz properties identified. Solutions preserving Lorentz invariance and ones breaking four of the six Lorentz generators are constructed. Locally, globally, and absolutely stable Lorentz-invariant extrema are found to exist for certain parameter ranges of the potential. Gravitational waves in the linearized theory are investigated. Deviations of the fiducial metric from the Minkowski metric are shown to lead to pentarefringence of the five wave polarizations, which can include superluminal modes and subluminal modes with negative energies in certain observer frames. The Newton limit of ghost-free massive gravity is explored. The propagator is constructed and used to obtain the gravitational potential energy between two point masses. The result extends the Fierz-Pauli limit to include corrections generically breaking both rotation and boost invariance.