Particular Solutions in Bimetric Theory and Their Implications

TL;DR

This paper investigates the dynamics of ghost-free bimetric theory, revealing conditions under which metrics are constrained to be Einstein or proportional, and exploring solutions that do not reduce to massive gravity, with implications for partially massless symmetry.

Contribution

It identifies specific constraints linking Einstein metrics in bimetric theory and explores solutions lacking a massive gravity limit, advancing understanding of the theory's solution space.

Findings

Einstein metrics in one metric imply Einstein in the other

Certain models avoid pathological solutions with singularities

Existence of solutions without a massive gravity limit

Abstract

Ghost-free bimetric theory can describe gravity in the presence of an extra spin-2 field. We study certain aspects of dynamics in this theory: (1) It is shown that if either of the metrics is an Einstein solution then the other is always forced to be Einstein, too. For a class of bimetric models this constraint is stronger and as soon as one metric is Einstein, the other metric is forced to be proportional to it. As a consequence, the models in this class avoid a branch of pathological solutions that exhibit determinant singularities or nonlinear ghosts. These constraints persists in a generalized form when sources are included, but are destroyed in the massive gravity limit of the theory. (2) For another class of bimetric models, we show the existence of solutions that do not admit a massive gravity limit. A bimetric model that could exhibit a nonlinear version of "partially massless" symmetry belongs to both these classes. It is argued that if such a model exits, its symmetry will not survive in the massive gravity limit.