Latest paper
Binary Ellis–Bronnikov Wormholes
Mergers, Fly-bys and Gravitational Waves in 3+1 Numerical Relativity
- Authors
- Nikita M. Shirokov and Ilya Nachevsky
- Submitted
- 9 Oct 2026
- arXiv
- Submitted, link to follow
- Code & data DOI
- 10.5281/zenodo.23257999
- GPU time
- 592 H100-hours, 103 evolutions
In brief
A traversable wormhole held open by a phantom scalar field is unstable: nudge it outward and the throat collapses into a black hole, squeeze it and the throat blows open. We followed a single Ellis–Bronnikov wormhole down both roads in full 3D numerical relativity. The black hole it becomes shrinks as it swallows the field that held the throat open — Hawking’s area law run backwards.
Then we put two in one universe. Like scalar charges repel and opposite charges attract, so only opposite pairs fall together. Head-on, one horizon forms around both still-open throats and settles toward a black hole of the pair’s mass; with orbital momentum a pair merges, plunges to a merged core, or flies past while both of its mouths inflate. Every encounter radiates one burst of gravitational waves — never an inspiral chirp, because no throat lives long enough to orbit.
Simulation time
t = 000
Horizon area
—
(a)Opposite charges fall together
Why it matters
First 3D simulations of wormhole binaries
Pairs of Ellis–Bronnikov wormholes in full 3+1 numerical relativity — head-on and off-axis mergers, fly-bys and plunges — to our knowledge for the first time.
Every throat collapses or inflates
The sign of the smallest nudge picks the fate, and the measured e-fold time matches linear theory to 1.9%: a stellar-mass throat is gone in milliseconds.
Two wormholes, one black hole
A common horizon forms around both open throats, born with their combined area, and swallows the phantom field that held them open.
A burst, never a chirp
No pair lives long enough to inspiral. Each encounter emits one burst of gravitational waves, plus a scalar dipole of negative energy that would pump the orbit, not drain it.
- Pull of opposite charges over the push of like ones, ±0.022, against the predicted 3/2 — so only opposite pairs merge.
- 1.462
- Area the common horizon loses as it swallows the phantom field. By t = 100 it is within 1.4% of the Schwarzschild radius.
- −28%
- Of a pair’s mass radiated as gravitational waves in the loudest fly-by, at the edge of capture.
- 7.6%
- Life of a 30 M☉ wormhole nudged by 1%. Ten more decades of quiet stretch it only to 19 ms.
- 1.6 ms
From one throat to a merger
One throat, two fates
A static Ellis–Bronnikov throat is a balance with a single unstable mode. Its e-fold time is one light-crossing of the throat, and the measured rate matches linear theory to 1.9%.
Whatever nudges it picks the ending, opposite to the push. Pushed outward, the throat collapses: a horizon forms, then loses 40% of its radius as it swallows the phantom field that held the throat open. Squeezed, the throat inflates — ×3.8 by t = 218, with no horizon in front of it.
ε > 0pushed out
ε < 0squeezed
Two identical throats, kicked in opposite directions, as embedding diagrams. Schematic. Like charges repel, opposite charges attract
Each throat carries a scalar charge, and the phantom field follows the electrostatic rule: like charges push apart, opposite charges pull together — 1.462 ± 0.022 times as hard, against the predicted 3/2. No separation, mass or speed lets a like pair fall together; it keeps receding while both of its mouths inflate.
An opposite pair falls together. Released 8 apart, its throats are still open when, at t = 18, one horizon closes around both, born with their combined area. The pair is now a black hole. Its horizon loses 28% of that area swallowing the phantom field; gravitational waves carry off only 4.7% of the loss.
+ +Like charges push apart
+ −Opposite charges fall together
Each lane one of the paper’s runs: a like pair released 12 apart, an opposite pair 8 apart. The arrows follow the measured force; field lines of point charges. Schematic. Merging is a race against inflation
A companion squeezes each mouth onto the inflation branch, so every merger is a race: the horizon must close before the throats blow open. The head-on’s arrives 3.5 e-folds in and wins; so does the d = 6 merger’s, at 2.5, though its pair carries orbital momentum.
At d = 12 the closest pass comes 9 e-folds in, too late: the pair flies by while both mouths inflate, or plunges to a merged core around which no common horizon is found. Fly-by and plunge part at 90–120% of the circular-orbit momentum.
The race clock counts e-folds of the throats’ unstable mode. Paths are schematic curves through the paper’s closest approaches and times. A burst, never a chirp
Black-hole binaries announce themselves with a chirp, orbit after orbit. A wormhole pair cannot: at d = 12 one orbit takes 75–93 units of time, and the companion’s squeeze leaves each throat about 28. Initial data quiet to one part in 10¹⁵ would buy only about two orbits.
Each encounter instead radiates one burst — a fly-by at the edge of capture sheds 7.6% of its mass, 73 times what two black holes on the same course radiate — while a scalar dipole of negative energy leaves beside it. Even a lone throat, collapsing out of round, sends out a burst that rings at the Schwarzschild frequency of the black hole it becomes. A burst with a drifting frequency and a scalar counterpart is the wormhole’s signature; a settled ringdown without one is already the black hole it became.
Each trace on its own scale, as in Fig. 8. Schematic.
Abstract
We present what are, to our knowledge, the first 3D numerical-relativity evolutions of wormhole binaries: pairs of massive Ellis–Bronnikov drainholes held open by a ghost scalar field. Each throat is an unstable fixed point whose e-fold time matches the González–Guzmán–Sarbach linear rate to within 1.9%. Two throats obey a charge-sign rule: like scalar charges repel and opposite charges attract, with a measured attraction-to-repulsion ratio of 1.462 ± 0.022 against the predicted 3/2, so only opposite-signed pairs merge. A head-on collision forms a common MOTS around both still-open throats, born with about their combined area. The horizon then loses 28% of its area as it swallows the phantom field, and by t = 100 lies within 1.4% of the Schwarzschild radius of the pair’s mass, still shrinking. Fly-by pairs form no horizon and both mouths inflate, the one nearest capture radiating the most gravitational-wave energy measured. A lone collapsing throat sheds its seeded quadrupole as a burst ringing at the Schwarzschild frequency of the black hole it becomes, and every encounter radiates its own burst of gravitational waves and a scalar dipole of comparable energy and negative sign. A throat survives at most a few orbital periods for any plausible perturbation, and the negative-energy dipole would pump rather than drain the orbit, so these binaries have no inspiral.
Figures from the paper
Simulation movies
A wormhole throat collapses into a black hole
Deformed out of round, the throat collapses; the new horizon swallows its own phantom support.
A wormhole throat blows open
Squeezed instead, the throat inflates and keeps growing, with no horizon in front of it.
Two wormholes collide head-on and form a black hole
Opposite charges released from rest at d = 8: one horizon closes around both open throats.
A wormhole fly-by
At p = 0.25 the pair swings past with no merger and no horizon, and both mouths inflate.
A deeper plunge
At p = 0.60 the mouths merge, and no horizon closes around them.
The hardest plunge
At p = 0.90 the mouths inflate as they merge.
Two wormholes with orbital momentum merge
At d = 6 with a small twist, the horizon wins the race against inflation and a black hole forms.
Control: two black holes collide head-on
The same collision with no exotic matter: the holes fall slower, and their bell carries 14× less energy.
Control: two black holes fly apart
Black holes at the fly-by’s separation and momentum are unbound and coast apart.
Control: two black holes plunge and merge
The vacuum twin climbs the familiar chirp. No wormhole pair does.
The head-on collision in a four-times-wider box
The head-on rerun to read its waves out to radius 150; the remnant spreads in coordinates while its area holds.
Two wormholes push each other apart
Like charges repel; as the pair recedes, both mouths inflate.
Cite
The paper is waiting for its arXiv number, which will appear here. Until then, cite it as below, with its code and data by their DOI.
Code · v1.0.1-wormhole-merger@misc{shirokov2026binary,
title = {Binary Ellis-Bronnikov wormholes in 3+1 numerical relativity: mergers, fly-bys and gravitational waves},
author = {Shirokov, Nikita M. and Nachevsky, Ilya},
year = {2026},
note = {Submitted to arXiv},
url = {https://www.firstinterstellarinstitute.com/research/binary-wormholes/}
}
@software{shirokov2026binary_code,
title = {GRTeclyn research fork --- colliding traversable wormholes},
author = {Shirokov, Nikita M. and Nachevsky, Ilya},
year = {2026},
version = {v1.0.1-wormhole-merger},
publisher = {Zenodo},
doi = {10.5281/zenodo.23257999},
url = {https://doi.org/10.5281/zenodo.23257999}
}