An Exact Solution of 4D Higher-Spin Gauge Theory

TL;DR

This paper presents a family of exact solutions in four-dimensional higher-spin gauge theory, revealing a rich structure of spacetime geometries with vanishing higher-spin fields and scalar-driven foliation between AdS and dS regions.

Contribution

It introduces a new class of exact solutions characterized by a zero-form invariant, expanding the understanding of higher-spin gauge theories and solution construction methods.

Findings

All higher-spin gauge fields vanish in the solutions.

The metric interpolates between AdS4, dS3, and Robertson-Walker spacetimes.

The scalar field acts as a foliation parameter.

Abstract

We give a one-parameter family of exact solutions to four-dimensional higher-spin gauge theory invariant under a deformed higher-spin extension of SO(3,1) and parameterized by a zero-form invariant. All higher-spin gauge fields vanish, while the metric interpolates between two asymptotically AdS4 regions via a dS3-foliated domainwall and two H3-foliated Robertson-Walker spacetimes -- one in the future and one in the past -- with the scalar field playing the role of foliation parameter. All Weyl tensors vanish, including that of spin two. We furthermore discuss methods for constructing solutions, including deformation of solutions to pure AdS gravity, the gauge-function approach, the perturbative treatment of (pseudo-)singular initial data describing isometric or otherwise projected solutions, and zero-form invariants.