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Anti-Self-Dual Spacetimes, Gravitational Instantons and Knotted Zeros of the Weyl Tensor

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arxiv 1904.06030 v3 pith:5EOFEJRN submitted 2019-04-12 hep-th gr-qcmath-phmath.MP

Snigdh Sabharwal , Jan Willem Dalhuisen This is my paper · ORCID
classification hep-thgr-qcmath-phmath.MP
keywords fieldsweylelectromagneticknottedlinkedmetricanti-self-dualcopy
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We derive a superpotential for null electromagnetic fields in which the field line structure is in the form of an arbitrary torus knot. These fields are shown to correspond to single copies of a class of anti-self-dual Kerr-Schild spacetimes containing the Sparling-Tod metric. This metric is the pure Weyl double copy of the electromagnetic Hopfion, and we show that the Eguchi-Hanson metric is a mixed Weyl double copy of this Hopfion and its conformally inverted state. We formulate two conditions for electromagnetic fields, generalizing torus knotted fields and linked optical vortices, that, via the zero rest mass equation for spin 1 and spin 2, defines solutions of linearized Einstein's equation possessing a Hopf fibration as the curves along which no stretching, compression or precession will occur. We report on numerical findings relating the stability of the linked and knotted zeros of the Weyl tensor and their relation to linked optical vortices.

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Cited by 4 Pith papers

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  1. Exact vacuum solution with Hopf structure in general relativity

    gr-qc 2025-06 conditional novelty 7.0 of 10

    A regular, two-parameter Petrov type D vacuum spacetime is constructed from a Hopf-fibration-derived null vector in Kerr-Schild form.

  2. Non-topological solitons in biadjoint scalar field theory

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    Biadjoint scalar theory admits a family of non-topological solitons carrying U(1) charge, time-dependent like Q-balls, stable in truncation, with finite localized energy.

  3. Hawking Radiation meets the Double Copy

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    Bogoliubov coefficients from scattering a scalar in a collapsing EM background (single copy of Vaidya) match ray-tracing results and connect to Hawking radiation through the double copy.

  4. Time-dependent solutions of biadjoint scalar field theories

    hep-th 2025-02 accept novelty 6.0 of 10

    New plane-wave-type exact solutions of generalized biadjoint scalar field theory are constructed, including bounded profiles, using elliptic, tanh, and rational functions.

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