Inconsistencies of massive charged gravitating higher spins

We examine the causality and degree-of-freedom (DoF) problems encountered by charged, gravitating, massive higher spin fields. For spin s = 3/2, making the metric dynamical yields improved causality bounds. These involve only the mass, the product eMP of the charge and Planck mass and the cosmological constant Λ. The bounds are themselves related to a gauge invariance of the timelike component of the field equation at the onset of acausality. While propagation is causal in arbitrary E/M backgrounds, the allowed mass ranges of parameters are of Planck order. Generically, interacting spins s > 3/2 are subject to DoF violations as well as to acausality; the former must be overcome before analysis of the latter can even begin. Here we review both difficulties for charged s = 2 and show that while a g-factor of 1/2 solves the DoF problem, acausality persists for any g. Separately we establish that no s = 2 theory — DoF preserving or otherwise — can be tree unitary.