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 gaugeequivalent to the extremal Didenko-Vasiliev solution [1]. The solutions activate all spins and can be characterized either via generalized electric and magnetic charges defined asymptotically in weakfield 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. suggest that higher-spin gravities are sub-sectors of particular tensionless limits of closed string field theories. Higher-spin gravities are thus tractable models for studying large-curvature effects in stringy completions of ordinary gravities.In particular, this opens a new window on holography in regimes where the boundary theories are weakly coupled and the bulk theories contain higher-spin gravities (and that are hence complementary to the more widely studied dual pairs involving strongly-coupled boundary theories and string theories with low-energy effective gravity descriptions on the bulk side). In this regime, the massless higherspin fields correspond to the bilinears in free fields on the boundary, which is a manifestation of the Vasiliev's equations [2,3] (see [4,5,6] for reviews) provide a fully nonlinear framework for higherspin gravities. They encode the classical dynamics of a highly complicated system -in which infinitely many fields of all spins are coupled through higher-derivative interaction vertices -into a combination 4 of zero-curvature constraints, for suitable master fields with simple higher-spin gauge transformations, and algebraic constraints, that actually describe a deformed ⋆-product algebra. This elegant description is achieved within the unfolded formulation of dynamics [14,15,4,5], which is a generalization based on differential algebras of the covariant Hamiltonian formulation of dynamics. The resulting unfolded systems consist of finitely many fundamental differential forms, which are the aforementioned master fields, living on extensions of spacetime referred to as correspondence spaces. Locally, these are products T * X × T , where X contains spacetime, and T is a non-commutative twistor space in the case of four-dimensional spacetime. The unexpected simplicity of the equations resides in that all spacetime component fields required for the unfolded formulation are packed away into the master fields in such a way that contractions of the coordinates of T , controlled by the deformed ⋆-p...

Abstract:We construct an infinite-dimensional space of solutions to Vasiliev's equations in four dimensions that are asymptotic to AdS spacetime and superpose massless scalar particle modes over static higher spin black holes. Each solution is obtained by a large gauge transformation of an all-order perturbatively defined particular solution given in a simple gauge, in which the spacetime connection vanishes, the twistor space connection is holomorphic, and all local degrees of freedom are encoded into the residual twistor space dependence of the spacetime zero-forms. The latter are expanded over two dual spaces of Fock space operators, corresponding to scalar particle and static black hole modes, equipped with positive definite sesquilinear and bilinear forms, respectively. Switching on an AdS vacuum gauge function, the twistor space connection becomes analytic at generic spacetime points, which makes it possible to reach Vasiliev's gauge, in which Fronsdal fields arise asymptotically, by another large transformation given here at first order. The particle and black hole modes are related by a twistor space Fourier transform, resulting in a black hole backreaction already at the second order of classical perturbation theory. We speculate on the existence of a fine-tuned branch of moduli space that is free from black hole modes and directly related to the quasi-local deformed Fronsdal theory. Finally, we comment on a possible interpretation of the higher spin black hole solutions as black-hole microstates.

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We formulate four dimensional higher spin gauge theories in spacetimes with signature (4 − p, p) and nonvanishing cosmological constant. Among them are chiral models in Euclidean (4, 0) and Kleinian (2, 2) signature involving half-flat gauge fields. Apart from the maximally symmetric solutions, including de Sitter spacetime, we find: (a) SO(4 − p, p) invariant deformations, depending on a continuous and infinitely many discrete parameters, including a degenerate metric of rank one; (b) non-maximally symmetric solutions with vanishing Weyl tensors and higher spin gauge fields, that differ from the maximally symmetric solutions in the auxiliary field sector; and (c) solutions of the chiral models furnishing higher spin generalizations of Type D gravitational instantons, with an infinite tower of Weyl tensors proportional to totally symmetric products of two principal spinors. These are apparently the first exact 4D solutions with non-vanishing massless higher spin fields.