Electromagnetic duality in general relativity

TL;DR

This paper explores electromagnetic-like duality in general relativity by analyzing the Riemann curvature's electric and magnetic parts, revealing symmetry properties and constructing dual solutions to vacuum and flat spacetimes.

Contribution

It introduces a duality relation in general relativity analogous to electromagnetism, linking Einstein vacuum solutions with sign-changing gravitational constants.

Findings

Vacuum equations are invariant under electric-magnetic interchange.

Dual solutions to vacuum and flat spacetimes can be constructed.

Duality symmetry implies Einstein vacuum equations without a cosmological constant.

Abstract

By resolving the Riemann curvature relative to a unit timelike vector into electric and magnetic parts, we consider duality relations analogous to the electromagnetic theory. It turns out that the duality symmetry of the Einstein action implies the Einstein vacuum equation without the cosmological term. The vacuum equation is invariant under interchange of active and passive electric parts giving rise to the same vacuum solutions but the gravitational constant changes sign. Further by modifying the equation it is possible to construct interesting dual solutions to vacuum as well as to flat spacetimes.