Hidden ghost in massive gravity

The Hessian's determinant for a version of massive gravity given by an infinite expansion of a square root function of the induced metric, vanishes. We show that it allows us to eliminate one of four scalar fields used to generate the graviton mass. This, however, gives rise to the appearance of extra terms in the action with the squared time derivative of the metric, thus signaling that a nonlinear ghost survives. We demonstrate this phenomenon considering a simple system with constraint, which is supposed to reduce the number of physical degrees of freedom, however, we explicitly show how the constraint forces the metric to propagate an extra tachyonic state.