Non-Einstein source effects in massive gravity

Abstract

We exhibit novel effects (absent in GR) of sources in massive gravity. First, we show that removing its ghost mode forces a field-current identity: The metric's trace is locally proportional to that of its stress tensor; a point source implies a metric singularity enhanced by the square of the graviton's range. Second, exterior solutions acquire spatial stress hair---their metric components depend on the interior ${T}_{ij}$. Also, in contrast to na\"{\i}ve expectations, the Newtonian potential of a source is now determined by both its spatial stress and mass. Our explicit results are obtained at linear, Fierz--Pauli, level but qualitatively persist nonlinearly.