Self-accelerating massive gravity: Bimetric determinant singularities

Abstract

The existence of two metrics in massive gravity theories in principle allows solutions where there are singularities in new scalar invariants jointly constructed from them. These configurations occur when the two metrics differ substantially from each other, as in black hole and cosmological solutions. The simplest class of such singularities are determinant singularities. We investigate whether the dynamics of bimetric massive gravity -- where the second metric is allowed to evolve jointly with the spacetime metric -- can avoid these singularities. We investigate whether the dynamics of bimetric massive gravity, where the second metric is allowed to evolve jointly with the spacetime metric, averts the simplest class of such singularities, namely determinant singularities. We show that it is still possible to specify non-singular initial conditions that evolve to a determinant singularity. Determinant singularities are a feature of massive gravity of both fixed and dynamical metric type.