Families of exact solutions to Vasiliev's 4D equations with spherical, cylindrical and biaxial symmetry
Abstract
We provide Vasiliev's four-dimensional bosonic higher-spin gravities with six families of exact solutions admitting two commuting Killing vectors. Each family contains a subset of generalized Petrov Type-D solutions in which one of the two mathfrak{s}mathfrak{o} (2) symmetries enhances to either mathfrak{s}mathfrak{o} (3) or mathfrak{s}mathfrak{o} (2, 1). In particular, the spherically symmetric solutions are static and we expect one of them to be gauge-equivalent to the extremal Didenko-Vasiliev solution [1]. The solutions activate all spins and can be characterized either via generalized electric and magnetic charges defined asymptotically in weak-field regions or via the values of fully higher-spin gauge-invariant observables given by on-shell closed zero-forms. The solutions are obtained by combining the gauge-function method with separation of variables in twistor space via expansion of the Weyl zero-form in Di-Rac supersingleton projectors times deformation parameters in a fashion that is suggestive of a generalized electromagnetic duality.
- Publication:
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Journal of High Energy Physics
- Pub Date:
- December 2011
- DOI:
- 10.1007/JHEP12(2011)084
- arXiv:
- arXiv:1107.1217
- Bibcode:
- 2011JHEP...12..084I
- Keywords:
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- Gauge Symmetry;
- Black Holes;
- Space-Time Symmetries;
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology
- E-Print:
- v1: 77 pages