  In this work we analyse the constraints imposed by Poincar\'e symmetry on the
gravitational form factors appearing in the Lorentz decomposition of the
energy-momentum tensor matrix elements for massive states with arbitrary spin.
By adopting a distributional approach, we prove for the first time
non-perturbatively that the zero momentum transfer limit of the leading two
form factors in the decomposition are completely independent of the spin of the
states. It turns out that these constraints arise due to the general Poincar\'e
transformation and on-shell properties of the states, as opposed to the
specific characteristics of the individual Poincar\'e generators themselves. By
expressing these leading form factors in terms of generalised parton
distributions, we subsequently derive the linear and angular momentum sum rules
for states with arbitrary spin.
