Exact spinning wormholes in five dimensions from Toda integrability

Abstract

We construct a new exact solution to the five-dimensional Einstein-phantom-scalar system that describes a rotating wormhole connecting two asymptotically flat regions. The solution represents a rotating generalization of the Ellis-Bronnikov wormhole with equal angular momenta. Under the cohomogeneity-one ansatz, we demonstrate that the radial equations reduce to an integrable $A_1\oplus A_2$ Toda system, from which the general local solution can be obtained in closed form. This integrable structure enables us to implement the regularity and asymptotic-flatness conditions analytically, thereby singling out a three-parameter family of solutions characterized by the mass, the equal angular momenta, and the scalar charge. The resulting spacetimes are geodesically complete, horizonless and stably causal, and contain no curvature singularities. The Toda structure further allows us to prove the uniqueness of the wormhole throat and to derive a sharp upper bound on the angular momentum for a fixed throat area. We also establish the existence and uniqueness of an ergosurface with respect to the stationary frame that is nonrotating at one asymptotic end, while the opposite end rotates relative to this frame. In a suitable scaling limit, the scalar field vanishes and the solution approaches the exterior region of the extremal Myers-Perry black hole with equal angular momenta.