Rotation slows the instability of Ellis-Bronnikov wormholes

Shirokov, Nikita M.; Nachevsky, Ilya

Spinning Ellis–Bronnikov Wormholes

Rotation Slows the Instability, in Nonlinear 3+1 Evolutions

Authors: Nikita M. Shirokov and Ilya Nachevsky
Published: 21 Oct 2026
arXiv: 2610.29941
Code & data DOI: 10.5281/zenodo.23245933
GPU time: 185 H100-hours, 19 evolutions

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Cite PDF Zenodo archive · DOI Code · v1.0-spinning-wormhole

In brief

An Ellis–Bronnikov wormhole — a throat held open by a phantom scalar field — is unstable: nudged, it collapses into a black hole or expands without bound. Rotation is the oldest hope for saving it. We built spinning wormholes as exact stationary solutions, up to 99% of light speed at the throat, and evolved them in full 3D general relativity: to our knowledge, the first nonlinear evolutions of a rotating wormhole.

Spin slows the collapse, as second-order perturbation theory predicts. Near 30% of the maximum angular momentum, where that theory suggested the instability would vanish, the throat expands instead. From 58% upward we see no growth over the evolved times, and at 81% the throat holds to t = 150 at three resolutions. A spinning collapse also sends out a burst of gravitational waves with nothing added to disturb it; a static one sends out nothing.

Throat speed

0.00 c

Exotic matter left

100%

(a)At rest

Instability growth rate

At rest: collapses

AnimationThe drainhole spun up from rest to a throat speed of 0.99 c, every step a solution from our solver. Dots are space dragged around by the spin; red grains are the exotic matter holding the throat open, a fixed amount per unit of throat size, so fewer remain as it spins. Drawn at a fixed zoom: the throat ring keeps one size while the throat itself grows. Bottom right: the instability’s growth rate in the 3D runs, the white dot at the current speed. The collapse slows along the paper’s fit to the runs (dots); dashed, the fit extrapolated to zero, a range where the runs expand instead or cannot be measured; rings, the runs from 0.75 c to 0.90 c, which show no growth.

Why it matters

First nonlinear evolutions of a spinning wormhole
To our knowledge no rotating wormhole had been evolved nonlinearly. We evolved the drainhole at nine spins in full 3+1 numerical relativity, perturbed only by truncation error.
Exact spinning backgrounds to 0.99 c
A spectral solver built the drainhole family, which had no published fast-spin solutions, and checked every solution against identities it never uses. Those checks caught an error in a published field equation.
Spin slows the collapse, then the throat expands
The e-fold time grows from 5.4 at rest to 13.3 at 24% of the maximum angular momentum. Near 30%, instead of the conjectured mode merger, the unperturbed throat expands at a rate that rises with spin.
No growth at fast spin
From 58% upward the throat shows no growth within the converged spans; at 81% it holds to t = 150 at three resolutions. The runs bound only axisymmetric growth, and only that long.

E-fold time of the collapse at 24% of the maximum angular momentum, against 5.4 at rest: spin slows the instability.: 13.3
Of the maximum angular momentum, where the unperturbed throat turns to expansion instead of the conjectured end of the instability.: ≈30%
No growth within the converged spans. At 81% the throat holds to t = 150, about 28 e-folds of the static mode, at three resolutions.: 58%+
Exotic matter per unit of throat radius left at 0.99 c along the drainhole family: a hundredfold less than at rest.: 1%

Spin a wormhole up, then evolve it

01
Spin a wormhole up
No closed form describes a spinning wormhole, so we built them as exact stationary solutions with a spectral solver: 462 solutions in 20 continuation sweeps, 200 of them on the paper’s two families, both reaching 99% of light speed at the throat. Every one was tested against five identities the solver never uses — checks that exposed an error in a published field equation.
Spin flattens the throat, drags space around it and, per unit of throat radius, needs far less exotic matter: a hundredfold less along the lopsided drainhole family and tenfold less along the symmetric one by 0.99 c. Both families end on an extremal Kerr black hole, and both exceed the Kerr bound — the symmetric one at every spin, the drainhole by up to 20% — so a collapsing throat cannot settle into a Kerr black hole of the same mass and spin.
02
Spin slows the instability
We evolved the drainhole at nine spins in full 3+1 numerical relativity, with nothing added to disturb it but the grid’s own truncation error. At rest the throat collapses into a black hole. Spin slows that collapse: the e-fold time grows from 5.4 to 13.3 by 24% of the maximum angular momentum, and the rate extrapolates to zero at 32%, beside second-order theory’s 33%.
The instability does not end there. Near 30% the unperturbed throat expands instead, at a rate that rises with spin — not the mode merger that perturbation theory conjectured. From 58% upward no growth appears within the converged spans; at 81% the throat holds to t = 150, about 28 e-folds of the static mode, at three resolutions. The runs bound only axisymmetric growth: above 29% the throat’s equator lies in an ergoregion, which leaves room for a slow non-axisymmetric instability.
Spin also makes the collapse radiate. With nothing put in to break its symmetry, a spinning throat sends out one (2,0) burst of gravitational waves, its energy per unit mass growing from 3.3 to 8.0 × 10⁻⁷ between 0.21 c and 0.30 c. The static collapse is perfectly round and sends out nothing.
Pick a run to watch it; drag on a chart to scrub. Time is in units where the wormhole at rest has mass 1.
The 3D runs

Abstract

We present nonlinear 3+1 evolutions of rotating Ellis–Bronnikov wormholes. We construct stationary rotating drainhole solutions with a spectral solver up to an equatorial rotation velocity of 99% of the speed of light, validate the solver against published symmetric solutions, and correct an inconsistency in a published field equation. Perturbed only by truncation error, the evolutions show that rotation slows the radial instability of the static wormhole. Near 30% of the extremal angular momentum the unperturbed throat expands instead of collapsing, rather than the instability disappearing as second-order perturbation theory suggests. From 58% upward we find no evidence of instability over the evolved times; at the fastest spin this holds at three resolutions. Collapsing rotating throats emit an axisymmetric quadrupolar gravitational-wave burst whose energy grows with spin. Second-order perturbative initial data trigger the instability through their own truncation error, so they are unsuitable for stability studies.

11 pages, 7 figures, 5 tables · gr-qc, astro-ph.HE

Figures from the paper

Full paper

Spinning wormholes, Fig. 3 — The two spinning families against the throat’s speed: mass, angular momentum and throat radius, the Kerr bound both exceed, the end-mass ratio, the flattening, the exotic matter per unit of throat radius and the throat’s angular velocity. — Fig. 3The two spinning families against the throat’s speed: mass, angular momentum and throat radius, the Kerr bound both exceed, the end-mass ratio, the flattening, the exotic matter per unit of throat radius and the throat’s angular velocity. Both end on extremal Kerr.

Spinning wormholes, Fig. 4 — The growth rate against angular momentum. — Fig. 4The growth rate against angular momentum. The collapses follow second-order theory at slow spin and fall below it faster; near 30% the throat expands instead (triangles), and from 58% no growth is seen (rings).

Spinning wormholes, Fig. 5 — The (2,0) gravitational-wave burst of the unperturbed spinning collapse: on spheres out to R = 45, against spin, the energy it carries, and the speed of each crest against light. — Fig. 5The (2,0) gravitational-wave burst of the unperturbed spinning collapse: on spheres out to R = 45, against spin, the energy it carries, and the speed of each crest against light.

Spinning wormholes, Fig. 7 — The fastest model, at 81% of the maximum angular momentum, at three resolutions to t = 150: the constraints converge, the throat radius holds, and no wave appears. — Fig. 7The fastest model, at 81% of the maximum angular momentum, at three resolutions to t = 150: the constraints converge, the throat radius holds, and no wave appears.

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Code · v1.0-spinning-wormhole

BibTeX

@misc{shirokov2026rotation,
  title         = {Rotation slows the instability of Ellis-Bronnikov wormholes},
  author        = {Shirokov, Nikita M. and Nachevsky, Ilya},
  year          = {2026},
  eprint        = {2610.29941},
  archivePrefix = {arXiv},
  primaryClass  = {gr-qc},
  url           = {https://arxiv.org/abs/2610.29941}
}

@software{shirokov2026rotation_code,
  title     = {GRTeclyn research fork --- colliding and rotating traversable wormholes},
  author    = {Shirokov, Nikita M. and Nachevsky, Ilya},
  year      = {2026},
  version   = {v1.0-spinning-wormhole},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.23245933},
  url       = {https://doi.org/10.5281/zenodo.23245933}
}

In brief

Spin a wormhole up, then evolve it

Spin a wormhole up

Spin slows the instability

Abstract

Figures from the paper

Cite