Abstract
It has been shown that the spherically symmetric solutions in a subclass of quasidilaton theory are stable against all degrees of freedom and does not even exhibit superluminal propagation. These solutions can be found by switching off scalar-tensor interactions, which can not be removed by a local transformation. In this paper, we extend the analysis to quasidilaton theory, including non-diagonalizable scalar-tensor interactions. We show that all solutions inside the Vainshtein radius are problematic : the scalar mode in massive graviton suffers from gradient instabilities, the vector mode are infinitely strongly coupled vector perturbations, or the Vainshtein mechanism is absent.
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