Non-locality and gravitoelectromagnetic duality

Abstract

The weak-field Schwarzschild and NUT solutions of general relativity are gravitoelectromagnetically dual to each other, except on the positive $z$-axis. The presence of non-locality weakens this duality and violates it within a smeared region around the positive $z$-axis, whose typical transverse size is given by the scale of non-locality. We restore an exact non-local gravitoelectromagnetic duality everywhere via a manifestly dual modification of the linearized non-local field equations. In the limit of vanishing non-locality we recover the well-known results from weak-field general relativity.