Abstract
We study linear perturbations around time dependent spherically symmetric solutions in the Λ3 massive gravity theory, which self-accelerate in the vacuum. We find that the dynamics of the scalar perturbations depend on the choice of the fiducial metric for the background solutions. For particular choice of fiducial metric there is a symmetry enhancement, leaving no propagating scalar degrees of freedom at linear order in perturbations. In contrast, any other choice propagates a single scalar mode. We find that the Hamiltonian of this scalar mode is unbounded from below for all self-accelerating solutions, signalling an instability.
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