Torsion-induced gravitational $\theta$ term and gravitoelectromagnetism

Understand

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.