  Motivated by the analogy between a weak field expansion of general relativity
and Maxwell's laws of electrodynamics, we explore physical consequences of a
parity violating $\theta$ term in gravitoelectromagnetism. This is distinct
from the common gravitational $\theta$ term formed as a square of the Riemann
tensor. Instead it appears as a product of the gravitoelectric and
gravitomagnetic fields in the Lagrangian, similar to the Maxwellian $\theta$
term. We show that this sector can arise from a quadratic torsion term in
nonlinear gravity. In analogy to the physics of topological insulators, the
torsion-induced $\theta$ parameter can lead to excess mass density at the
interface of regions where $\theta$ varies and consequently it generates a
correction to Newton's law of gravity. We discuss also an analogue of the
Witten effect for gravitational dyons.
