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

Understand

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.