Biaxially symmetric solutions to 4D higher-spin gravity

TL;DR

This paper reviews biaxially symmetric solutions in 4D higher-spin gravity, highlighting their construction via gauge functions and their relation to charges and invariants, advancing understanding of exact solutions in higher-spin theories.

Contribution

It introduces a method to construct biaxially symmetric solutions in 4D higher-spin gravity using gauge functions, projectors, and deformed oscillators, and relates deformation parameters to physical charges.

Findings

Solutions activate all bosonic spins.

Deformation parameters relate to electric and magnetic charges.

Zero-form charges serve as higher-spin Casimir invariants.

Abstract

We review some aspects of biaxially symmetric solutions to Vasiliev's equations in four dimensional spacetime with negative cosmological constant. The solutions, which activate bosonic fields of all spins, are constructed using gauge functions, projectors and deformed oscillators. The deformation parameters, which are formally gauge invariant, are related to generalized electric and magnetic charges in asymptotic weak-field regions. Alternatively, the solutions can be characterized in a dual fashion using zero-form charges which are higher-spin Casimir invariants built from combinations of curvatures and all their derivatives that are constant on shell and well-defined everywhere.