Particular solutions in bimetric theory and their implications

Abstract

Ghost-free bimetric theory can describe gravity in the presence of an extra spin-2 field. In this paper, we study certain aspects of dynamics in this theory: (i) 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. (ii) 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 exist, its symmetry will not survive in the massive gravity limit.