Iazeolla, CarloSezgin, ErginSundell, Per2022-09-232022-09-232018Universe Volume 4, Issue 1January 2018 Article number 522181997https://repositorio.unab.cl/xmlui/handle/ria/24036Indexación ScopusWe review various methods for finding exact solutions of higher spin theory in four dimensions, and survey the known exact solutions of (non)minimal Vasiliev's equations. These include instanton-like and black hole-like solutions in (A)dS and Kleinian spacetimes. A perturbative construction of solutions with the symmetries of a domain wall is also described. Furthermore, we review two proposed perturbative schemes: one based on perturbative treatment of the twistor space field equations followed by inverting Fronsdal kinetic terms using standard Green's functions; and an alternative scheme based on solving the twistor space field equations exactly followed by introducing the spacetime dependence using perturbatively defined gauge functions. Motivated by the need to provide a higher spin invariant characterization of the exact solutions, aspects of a proposal for a geometric description of Vasiliev's equation involving an infinite dimensional generalization of anti de Sitter space are revisited and improved. © 2018 by the authors.enChern-Simons TheoriesGauge TransformationSpinExact solutionsHigher-spin geometryHigher-spin gravityArtículoCC BY 4.010.3390/universe4010005