Anti-self-dual spacetimes, gravitational instantons and knotted zeros of the Weyl tensor
Abstract 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 i...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-07-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP07(2019)004 |
| _version_ | 1819163313705058304 |
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| author | Snigdh Sabharwal Jan Willem Dalhuisen |
| author_facet | Snigdh Sabharwal Jan Willem Dalhuisen |
| author_sort | Snigdh Sabharwal |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-12-22T17:42:09Z |
| format | Article |
| id | doaj.art-3d3e6b7f466547ea901c9be5e2349943 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-22T17:42:09Z |
| publishDate | 2019-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-3d3e6b7f466547ea901c9be5e23499432022-12-21T18:18:23ZengSpringerOpenJournal of High Energy Physics1029-84792019-07-012019711510.1007/JHEP07(2019)004Anti-self-dual spacetimes, gravitational instantons and knotted zeros of the Weyl tensorSnigdh Sabharwal0Jan Willem Dalhuisen1Huygens-Kamerlingh Onnes Laboratory, Leiden UniversityHuygens-Kamerlingh Onnes Laboratory, Leiden UniversityAbstract 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.http://link.springer.com/article/10.1007/JHEP07(2019)004Classical Theories of GravityGauge-gravity correspondenceSolitons Monopoles and Instantons |
| spellingShingle | Snigdh Sabharwal Jan Willem Dalhuisen Anti-self-dual spacetimes, gravitational instantons and knotted zeros of the Weyl tensor Journal of High Energy Physics Classical Theories of Gravity Gauge-gravity correspondence Solitons Monopoles and Instantons |
| title | Anti-self-dual spacetimes, gravitational instantons and knotted zeros of the Weyl tensor |
| title_full | Anti-self-dual spacetimes, gravitational instantons and knotted zeros of the Weyl tensor |
| title_fullStr | Anti-self-dual spacetimes, gravitational instantons and knotted zeros of the Weyl tensor |
| title_full_unstemmed | Anti-self-dual spacetimes, gravitational instantons and knotted zeros of the Weyl tensor |
| title_short | Anti-self-dual spacetimes, gravitational instantons and knotted zeros of the Weyl tensor |
| title_sort | anti self dual spacetimes gravitational instantons and knotted zeros of the weyl tensor |
| topic | Classical Theories of Gravity Gauge-gravity correspondence Solitons Monopoles and Instantons |
| url | http://link.springer.com/article/10.1007/JHEP07(2019)004 |
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