Electromagnetic duality in general relativity

Details Electromagnetic duality in general relativity Electromagnetic duality in general relativity

1999-09-21

arxiv.org/abs/gr-qc/9909067v1

Gen.Rel.Grav. 32 (2000) 1009-1023

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, LaTEX version

Scientific paper

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.

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