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.
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ArXiv ePrint: 1107.1217
F.R.S.-FNRS Researcher with an Ulysse Incentive Grant for Mobility in Scientific Research. (Per Sundell)
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Iazeolla, C., Sundell, P. Families of exact solutions to Vasiliev’s 4D equations with spherical, cylindrical and biaxial symmetry. J. High Energ. Phys. 2011, 84 (2011). https://doi.org/10.1007/JHEP12(2011)084
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DOI: https://doi.org/10.1007/JHEP12(2011)084