  In this work, we investigate modular Hamiltonians defined with respect to
arbitrary spatial regions in quantum field theory states which have
semi-classical gravity duals. We find prescriptions in the gravity dual for
calculating the action of the modular Hamiltonian on its defining state,
including its dual metric, and also on small excitations around the state.
Curiously, use of the covariant holographic entanglement entropy formula leads
us to the conclusion that the modular Hamiltonian, which in the quantum field
theory acts only in the causal completion of the region, does not commute with
bulk operators whose entire gauge-invariant description is space-like to the
causal completion of the region.
