Research

Published, with the code that produced it.

Every result goes to arXiv together with the source code, parameters and data needed to rerun it.

Latest paper9 Oct 2026gr-qc · astro-ph.HE592 GPU-hours

Binary Ellis–Bronnikov Wormholes

Mergers, Fly-bys and Gravitational Waves in 3+1 Numerical Relativity

Nikita M. Shirokov and Ilya Nachevsky · Submitted to arXiv

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.

Paper page

Zenodo archive · DOI Code · v1.0.1-wormhole-merger

Simulation time

t = 000

Horizon area

—

(a)Opposite charges fall together

AnimationThe head-on merger, after Fig. 6: opposite charges released from rest at d = 8. At t = 18 one horizon forms around both still-open throats, then loses 28% of its area as it swallows the phantom field. The times and the horizon’s size follow the paper; the sheet and the wave are schematic.

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

Figures from the paper

Binary wormholes, Fig. 1 — Fates of newborn throats. — Fig. 1Fates of newborn throats. A lone throat’s perturbation sign selects collapse or inflation, a pair’s relative sign repulsion or attraction; an attracting pair merges where its horizon outruns inflation, or plunges to a merged core.

Binary wormholes, Fig. 6 — The head-on merger. — Fig. 6The head-on merger. A common horizon (gold) forms around both open throats at t = 18, then shrinks toward the Schwarzschild sphere of the pair’s mass as the phantom field is swallowed.

Binary wormholes, Fig. 8 — The waveform gallery: one burst per scenario — collapsing throat, head-on, merger, fly-by, plunge — each set against black holes at the same separation and momentum (grey). — Fig. 8The waveform gallery: one burst per scenario — collapsing throat, head-on, merger, fly-by, plunge — each set against black holes at the same separation and momentum (grey).

Binary wormholes, Fig. 9 — Fig. 9Every source scaled to 30 M_☉ at 10 Mpc: no wormhole channel climbs the black-hole chirp, and the fly-by radiates the most energy of all.

Simulation movies

All 12 movies

Video 1

A wormhole throat collapses into a black hole

Deformed out of round, the throat collapses; the new horizon swallows its own phantom support.

Video 2

A wormhole throat blows open

Squeezed instead, the throat inflates and keeps growing, with no horizon in front of it.

Video 3

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.

Video 7

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.

Simulation time

t = 000

Pair speed

0.000c

AnimationThe phantom star (hill) chases the canonical star (well) that it repels, after Fig. 3. The motion follows the paper’s numbers — released at rest, constant acceleration, separation held at 10; the surface itself is schematic.

25 Aug 2026gr-qc · astro-ph.HE

The Bondi Dipole in Full Numerical Relativity

A Self-Accelerating Positive–Negative Mass Binary

Nikita M. Shirokov · arXiv:2608.24577

In 1957 Hermann Bondi showed that a negative mass and a positive mass, released side by side, set off together on their own: the positive mass pulls the negative one toward it, the negative mass pushes the positive one away, and the pair accelerates as one — with nothing expelled and no conservation law broken.

We put this “Bondi dipole” through full 3+1 numerical relativity, with a phantom scalar star as the negative mass. Across a campaign of thirty-four evolutions — runaway pairs, controls and parameter scans — the mixed pair accelerates as a unit, and the force behind it measures as gravity: inverse-square in separation, linear in mass.

Read on arXiv

Paper page PDF Code & campaign data

Why it matters

First 3D simulation of the Bondi dipole
Bondi’s 1957 runaway pair, evolved in full 3+1 numerical relativity across thirty-four runs.
First negative-mass star in numerical relativity
The phantom scalar star has negative ADM mass and survives on its own to t = 1000; we know of no earlier example.
Self-acceleration, confirmed in full general relativity
The pair reaches 0.056c from rest with nothing expelled, and its total momentum stays at zero.
The force is gravity
Inverse-square in separation and linear in mass, and the runaway radiates no detectable gravitational waves.

Speed the pair reaches from rest by t = 400, with the acceleration steady to 2%.: 0.056c
Measured force law over separations d = 8 to 20 — gravity’s inverse square, ±0.01.: d^−2.03
Swap which star is the phantom and the acceleration inverts, to two parts in 10⁵.: 2×10⁻⁵
Fall-off of the ℓ = 2 amplitude — a near-zone field, not a flux. The runaway radiates nothing detectable.: r^−4.8

Figures from the paper

Full paper

The Bondi dipole, Fig. 1 — Bondi’s sign rules. — Fig. 1Bondi’s sign rules. Inertia is positive for every body; only the active mass carries a sign. Like pairs fall together or push apart with the barycentre fixed — the mixed pair runs away.

The Bondi dipole, Fig. 3 — The runaway in the headline cell at t = 0, 60, 120, 200. — Fig. 3The runaway in the headline cell at t = 0, 60, 120, 200. Bottom row: χ − 1 — the phantom star is a hill, the canonical star a well. Both move toward +x while the gap holds to 1%.

The Bondi dipole, Fig. 4 — Core worldlines; a single constant-acceleration fit to the midpoint drift; the signal against every null run; and the Bondi signature — sector momenta grow while their signed sum holds at zero. — Fig. 4Core worldlines; a single constant-acceleration fit to the midpoint drift; the signal against every null run; and the Bondi signature — sector momenta grow while their signed sum holds at zero.

The Bondi dipole, Fig. 5 — Fig. 5Both axes of a = M̄/d², measured: acceleration ∝ d^{−2.03 ± 0.01} at fixed mass, and ∝ M̄^{0.97 ± 0.06} at fixed separation.

Simulation movies

Playlist

Video 1

A positive and a negative mass star accelerate themselves

The headline cell: the mixed pair released at rest, separation 10.

Video 2

The runaway does not stop: 400 time units

The same pair carried four times longer. The gap holds while the pair translates.

Video 3

Control: two positive-mass stars

They attract, fall together and merge — the centroid stays put.

Video 4

Control: two negative-mass stars

Gravity should push them apart; the shared field merges them anyway.

31 Mar 2026gr-qc · astro-ph.HE · hep-ex

Wormhole Dynamics

Nonlinear Collapse and Gravitational-Wave Emission

Nikita M. Shirokov · arXiv:2604.00071

We computed the first gravitational waves from a collapsing wormhole. The Ellis–Bronnikov wormhole — the classic traversable solution, held open by a phantom scalar field — is unstable, and we followed its collapse in full 3D numerical relativity.

Weakened and nudged out of spherical symmetry, the throat collapses, a trapped surface forms and the event emits gravitational waves. The phantom matter swallowed by the new horizon then rebounds, launching an outward curvature shock.

Read on arXiv

Paper page PDF Source & extraction data

(a)Traversable throat

S_support = 0.5 · A_φ = +0.02

AnimationThe compressive pathway, after Fig. 1 (S_support = 0.5, A_φ = +0.02). Classical evolution keeps the spatial topology intact: “pinch-off” means the throat’s areal radius collapses as an apparent horizon forms, cutting the two sides off from each other.

Why it matters

First gravitational waves from a collapsing wormhole
In full 3D numerical relativity, the Ellis–Bronnikov throat, nudged out of spherical symmetry, collapses behind a new horizon and radiates.
Real radiation, not a numerical artefact
The waveform peak crosses the extraction radii at 0.995c, unlike the faster-than-light constraint modes of the CCZ4 equations.
The phantom bounce
After the horizon forms, the phantom matter it swallowed rebounds and launches an outward curvature shock.
A target for detectors
A 10³ M☉ wormhole 1 Mpc away would peak at 100–300 Hz, just below Advanced LIGO’s design sensitivity; closer sources or next-generation detectors could catch it.

Gravitational waves from a collapsing wormhole, computed in full 3D numerical relativity.: First
Speed of the waveform peak between extraction radii R = 12 and 16 — physical radiation, not a gauge mode.: 0.995c
An apparent horizon closes off the throat; the phantom matter it swallows rebounds and launches an outward curvature shock.: Bounce
At 1 Mpc, the signal peaks at 100–300 Hz, just below Advanced LIGO design sensitivity.: 10³ M_☉

Figures from the paper

Full paper

Wormhole dynamics, Fig. 1 — Embedding diagrams of the two instability pathways: compressive collapse to pinch-off (top) and rarefactive expansion (bottom). — Fig. 1Embedding diagrams of the two instability pathways: compressive collapse to pinch-off (top) and rarefactive expansion (bottom).

Wormhole dynamics, Fig. 3 — Diagnostics of the perturbed collapse: the throat radius plunges and rebounds, and an apparent horizon forms, inflates in the phantom bounce, then is destroyed by the shock. — Fig. 3Diagnostics of the perturbed collapse: the throat radius plunges and rebounds, and an apparent horizon forms, inflates in the phantom bounce, then is destroyed by the shock.

Wormhole dynamics, Fig. 4 — Ψ₄ extraction for the perturbed collapse: waveforms aligned in retarded time, spectrum, propagation speed, spectrogram, and strain against Advanced LIGO. — Fig. 4Ψ₄ extraction for the perturbed collapse: waveforms aligned in retarded time, spectrum, propagation speed, spectrogram, and strain against Advanced LIGO.

All publications

3 papers

9 Oct 2026
Submitted to arXiv
Binary Ellis-Bronnikov wormholes in 3+1 numerical relativity: mergers, fly-bys and gravitational waves
Nikita M. Shirokov and Ilya Nachevsky · 25 pages, 12 figures, 12 movies · gr-qc, astro-ph.HE
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.
DOI Code
25 Aug 2026
arXiv:2608.24577
The Bondi Dipole in Full Numerical Relativity: a Self-Accelerating Positive-Negative Mass Binary
Nikita M. Shirokov · 13 pages, 10 figures, 4 ancillary movies · gr-qc, astro-ph.HE
Abstract
Bondi showed in 1957 that bodies of opposite active gravitational mass self-accelerate: the negative chases the positive it repels, and the pair runs off together. We evolve this “Bondi dipole” in 3+1 numerical relativity: two complex scalars share identical Klein–Gordon dynamics; only the phantom enters Einstein’s equations with a minus sign — inertial and passive masses positive, active mass negative. Across a matrix of thirty-four evolutions — runaway pairs, controls, and parameter scans — a mass-matched pair released at rest accelerates as a unit. The midpoint moves 3.00 ± 0.01 by t = 200 with the separation held to 1%, and reaches a speed of 0.056c by t = 400 with the acceleration steady to 2%; the total signed momentum holds at zero to ≲ 1%. The force is gravity on both of its axes: a ∝ d^{−2.03 ± 0.01} over d = 8 to 20, a ∝ M^{0.97 ± 0.06} over a factor 2.5 in mass, and a d²/M̄ = 1 within 2.4% on the equal-mass ladder. Swapping the sectors inverts the acceleration to two parts in 10⁵; gauge, solver-depth and mesh variations move the drift by ≲ 0.01% and box doubling by 4%; same-sign control pairs hold their centroids to ≲ 8 × 10⁻⁴ even while merging. The runaway carries no detectable gravitational radiation: the signed dipole cannot radiate, the quadrupole’s Q̈ is constant, and the measured ℓ = 2 amplitude falls as r^−4.8 — near zone, not flux. The phantom star is, to our knowledge, the first asymptotically flat body of negative ADM mass evolved in numerical relativity; alone it survives to t = 1000, slowly relaxing outward.
arXiv PDF Code
31 Mar 2026
arXiv:2604.00071
Wormhole Dynamics: Nonlinear Collapse and Gravitational-Wave Emission
Nikita M. Shirokov · 13 pages, 7 figures · gr-qc, astro-ph.HE, hep-ex
Abstract
We present 3D numerical-relativity evolutions of the unstable Ellis–Bronnikov wormhole using GRTeclyn, starting from exact isotropic initial data for the coupled Einstein–phantom-scalar system. With a flat initial lapse (α = 1) and full phantom support, truncation-level noise eventually drives the rarefactive instability and rapid throat expansion. To force a clean collapse while breaking spherical symmetry, we reduce the phantom stress-energy support to S_support = 0.5 and add a quadrupolar scalar-field perturbation (A_φ = +0.02, σ_φ = 0.5). The resulting compressive evolution forms a trapped surface and emits a gravitational-wave signal whose peak propagates between extraction radii at v ≈ c, distinct from superluminal CCZ4 constraint modes. After horizon formation the swallowed phantom matter triggers a violent rebound (“phantom bounce”) that launches an outward curvature shock. For the moderate perturbation amplitude simulated here, an intermediate-mass (10³ M_☉) wormhole at D = 1 Mpc falls slightly below the Advanced LIGO design sensitivity; detection requires either closer sources, larger initial asymmetries, or next-generation detectors.
arXiv PDF Code