Gravoelectric-dual of the Kerr solution

Details Gravoelectric-dual of the Kerr solution Gravoelectric-dual of the Kerr solution

1999-09-21

arxiv.org/abs/gr-qc/9909066v1

J.Math.Phys. 41 (2000) 882-890

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, LaTEX version

Scientific paper

By decomposing the Riemann curvature into electric and magnetic parts, we define the gravoelectric duality transformation by interchange of active and passive electric parts which amounts to interchange of the Ricci and Einstein tensors. It turns out that the vacuum equation is duality-invariant. We obtain solutions dual to the Kerr solution by writing an effective vacuum equation in such a way that it still admits the Kerr solution but is not duality invariant. The dual equation is then solved to obtain the dual-Kerr solution which can be interpreted as the Kerr black hole sitting in a string dust universe.

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