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Non-locality and gravitoelectromagnetic duality

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arxiv 2103.10555 v1 pith:3SAJQHMT submitted 2021-03-18 gr-qc

Jens Boos , Ivan Kolář This is my paper · ORCID
classification gr-qc
keywords non-localitydualityaxisdualgeneralgravitoelectromagneticnon-localpositive
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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.

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  1. What happens to topological invariants (and black holes) in singularity-free theories?

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    Regularizing point-source singularities makes flat-space topological charges radius-dependent; in general relativity the same idea gives a cut-out Reissner-Nordström geometry with finite low-order curvature invariants.

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