Exact Rotating Wormholes in Five Dimensions and Their Exceptional-Point Instability

Abstract

We give an independent closed-form construction of rotating five-dimensional Ellis--Bronnikov wormholes with equal angular momenta and analyze the radial instability of the reflection-symmetric family. The nontrivial coupled metric equations reduce exactly to an open $A_2$ Toda system. The general two-ended solution is expressed in terms of elementary Toda tau functions; the symmetric subclass reduces to a particularly simple one-parameter family interpolating between the static wormhole and the extremal equal-spin Myers--Perry geometry. On this exact background we revisit the cohomogeneity-one perturbation problem. Besides the ordinary unstable mode of the static wormhole, rotation renders the descendant of its non-normalizable zero mode normalizable. The two purely imaginary unstable frequencies coalesce at $|J|/A=0.100628$, where their eigenvectors coalesce as well, identifying a second-order exceptional point. Beyond it the pair continues as $ω_\pm=\pmω_R+\mathrm iω_I$ with $ω_I>0$: the apparent loss of the radial instability found in the original real-eigenvalue treatment is therefore not stabilization, but a transition to an oscillatory instability. We follow this branch deep into the rapidly rotating regime, where its growth rate becomes strongly suppressed.