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

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 AdS 4 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.

4D higher spin black holes with nonlinear scalar fluctuations

“…Black-hole-like solutions of the Vasiliev equations have been constructed in [1][2][3]91], but the present lack of a stringy generalization of geometry has so far limited our capability to assess their precise nature -for instance by establishing whether they possess a horizon, whether their curvature singularity is physical or not, etc. Moreover, whereas the Type-D solution spaces in ordinary gravity are finite-dimensional, it was observed in [1,2] that their higher-spin counterparts are infinite-dimensional.…”

“…In particular, all Weyl tensors share the Killing symmetries, Petrov type D and principal spinors of the latter; 2 see [3] for the first instance of such a solution, and [1,2,91] for developments. In gravity, such a form of the Weyl tensor is a local hallmark of a black-hole solution [68].…”

“…This system can be treated in two dual fashions, by either reducing it perturbatively to deformed set of Fronsdal fields on spacetime [4,7,9,84,92], or expressing the fields using a gauge function (i.e. a large gauge transformation) and a set of deformed oscillators constructed using algebraic methods [1,9,66,67,85,87,91].…”

“…In a previous work [1] (see also [2,91]), we have used the latter method to construct families of exact generalized Petrov Type D solutions, encompassed by an Ansatz based on factorization of noncommutative fiber and base twistor coordinates, absorbed into generalized projectors and deformed oscillators, respectively. The various families are distinguished by different Killing symmetries, while all share the Kerr-Schild property, i.e., the full Weyl zero-form coincides with the linearized one (in a special gauge).…”

“…In the black hole sector, the resulting t-integral was analyzed in [91], and shown to be a real-analytic function on C for r > 0, and to reproduce 72) that is, the linearized internal connection obtained by direct integration in the Vasiliev gauge, recalling that the linearized Weyl zero-form is the same in the L and Vasiliev gauges; see, for example, [8,84]. At r = 0 the internal connection is instead singular, as expected.…”