New classes of bi-axially symmetric solutions to four-dimensional Vasiliev higher spin gravity

TL;DR

This paper introduces new infinite-dimensional bi-axially symmetric solutions to four-dimensional Vasiliev higher spin gravity, expanding the known solution space with novel algebraic and geometric structures.

Contribution

It develops a modified Ansatz using internal semigroup algebras to find new solutions with specific symmetry and asymptotic properties in Vasiliev higher spin gravity.

Findings

Solutions exhibit Kerr-like and 2-brane-like structures in AdS4.

The generalized Weyl tensor is a sum of Petrov type-D tensors.

Twistor space connection is smooth and can be gauge-fixed to Vasiliev gauge.

Abstract

We present new infinite-dimensional spaces of bi-axially symmetric asymptotically anti-de Sitter solutions to four-dimensional Vasiliev higher spin gravity, obtained by modifications of the Ansatz used in arXiv:1107.1217, which gave rise to a Type-D solution space. The current Ansatz is based on internal semigroup algebras (without identity) generated by exponentials formed out of the bi-axial symmetry generators. After having switched on the vacuum gauge function, the resulting generalized Weyl tensor is given by a sum of generalized Petrov type-D tensors that are Kerr-like or 2-brane-like in the asymptotic AdS4 region, and the twistor space connection is smooth in twistor space over finite regions of spacetime. We provide evidence for that the linearized twistor space connection can be brought to Vasiliev gauge.