Algebraic properties of Einstein solutions in ghost-free bimetric theory

A fact is that an Einstein solution in one sector in ghost-free bimetric theory implies an Einstein solution in the other sector. Earlier studies have also shown that some classes of bimetric models necessitate proportional solutions between the sectors. Here, we consider a general setup of the parameters in the theory as well as the general algebraic form of the potential. We show that, if one sector has an Einstein solution, the solutions are either proportional or block proportional with at most two different eigenvalues in the square root governing metric interactions. Published under license by AIP Publishing.