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

TL;DR

This paper constructs six families of exact solutions to four-dimensional Vasiliev higher-spin gravity equations, revealing new symmetric configurations with potential physical interpretations and gauge equivalences.

Contribution

It introduces a systematic method to generate exact solutions with various symmetries in Vasiliev's higher-spin gravity, including spherically symmetric cases.

Findings

Six families of exact solutions with two commuting Killing vectors.

Solutions include generalized Petrov Type-D configurations.

Activation of all spins with gauge-invariant characterization.

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 so(2) symmetries enhances to either so(3) or so(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 given in arXiv:0906.3898. 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.