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Families of exact solutions to Vasiliev’s 4D equations with spherical, cylindrical and biaxial symmetry

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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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Authors and Affiliations

  1. Dipartimento di Fisica, Università di Bologna and INFN, Sezione di Bologna, via Irnerio 46, I-40126, Bologna, Italy

    Carlo Iazeolla

  2. Service de Mécanique et Gravitation, Université de Mons, Place du Parc, 20, 7000, Mons, Belgium

    Per Sundell

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  1. Carlo Iazeolla
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  2. Per Sundell
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Correspondence to Carlo Iazeolla.

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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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