RECORD
The Bondi dipole in full numerical relativity: a self-accelerating positive-negative mass binary
General Relativity and Quantum Cosmology · Submitted 25 Aug 2026
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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 compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
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 $3.00\pm0.01$ 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 $\lesssim 1$%. The force is gravity on both of its axes: $a\propto d^{-2.03\pm0.01}$ over $d=8$ to $20$, $a\propto M^{0.97\pm0.06}$ over a factor $2.5$ in mass, and $a\,d^2/\bar{M}=1$ within 2.4% on the equal-mass ladder. Swapping the sectors inverts the acceleration to two parts in $10^5$; gauge, solver-depth and mesh variations move the drift by $\lesssim 0.01$% and box doubling by 4%; same-sign control pairs hold their centroids to $\lesssim 8\times10^{-4}$ even while merging. The runaway carries no detectable gravitational radiation: the signed dipole cannot radiate, the quadrupole's $\ddot{Q}$ is constant, and the measured $\ell=2$ 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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | background 1.00 | 0.02 | 0.22 | asserted 1.00 |
| s1 | 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. | method 0.62 | 0.90 | 0.08 | asserted 0.99 |
| s2 | Across a matrix of thirty-four evolutions -- runaway pairs, controls, and parameter scans -- a mass-matched pair released at rest accelerates as a unit. | result 0.61 | 0.95 | 0.46 | asserted 1.00 |
| s3 | The midpoint moves $3.00\pm0.01$ 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 $\lesssim 1$%. | result 1.00 | 0.96 | 0.21 | asserted 1.00 |
| s4 | The force is gravity on both of its axes: $a\propto d^{-2.03\pm0.01}$ over $d=8$ to $20$, $a\propto M^{0.97\pm0.06}$ over a factor $2.5$ in mass, and $a\,d^2/\bar{M}=1$ within 2.4% on the equal-mass ladder. | result 1.00 | 0.96 | 0.11 | asserted 1.00 |
| s5 | Swapping the sectors inverts the acceleration to two parts in $10^5$; gauge, solver-depth and mesh variations move the drift by $\lesssim 0.01$% and box doubling by 4%; same-sign control pairs hold their centroids to $\lesssim 8\times10^{-4}$ even while merging. | result 0.98 | 0.96 | 0.07 | asserted 1.00 |
| s6 | The runaway carries no detectable gravitational radiation: the signed dipole cannot radiate, the quadrupole's $\ddot{Q}$ is constant, and the measured $\ell=2$ amplitude falls as $r^{-4.8}$ -- near zone, not flux. | result 0.96 | 0.94 | 0.12 | asserted 1.00 |
| s7 | 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. | result 0.58 | 0.92 | 0.15 | asserted 0.94 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
Bondi showed in 1957 that a body of negative active gravitational mass and a positive one should accelerate together without limit while their total momentum stays zero. We test this prediction in full 3+1 numerical relativity, from constraint-satisfying initial data. The matter is two complex scalar fields with identical self-interactions, one of which enters the Einstein equations with the opposite sign; its stars have positive inertial and passive masses but negative active and Arnowitt-Deser-Misner (ADM) masses. To our knowledge, they are the first asymptotically flat bodies of negative ADM mass evolved in numerical relativity. A pair of stars with equal and opposite ADM masses accelerates as a single object at constant separation, and its total momentum stays zero to within 0.5%. The acceleration follows Newton's law of gravitation in both mass and separation, reverses when the stars are exchanged, and is absent in same-sign pairs and isolated stars. We detect no gravitational radiation. The results hold for head-on pairs released from rest, up to a few percent of the speed of light, and in the longest run the pair reaches a tenth of it with both stars intact.
Human review
References
How the literature uses it
What this paper does with the arXiv papers it cites
What it cites · 6 sentences without a confident label
Uses the method or tool of 3 papers
-
[ref] then re-solves the constraints for the pair (CTTK family [ref] , sources summed with their signs star by star).
GRTresna: An open-source code to solve the initial data constraints in numerical relativity · Two construction requirements · 0.93
-
Every evolution ran on GPUs with [ref] , the AMReX-based [ref] GPU port of [ref] ; with the wormhole campaign of Ref. [ref] these are, to our knowledge, the first evolutions of energy-condition-violating matter in GPU-native numerical relativity, the warp-bubble collapse of Ref. [ref] being the closest CPU-side precedent.
What no one has seen before: gravitational waveforms from warp drive collapse · Introduction · 1.00
-
Every evolution ran on GPUs with [ref] , the AMReX-based [ref] GPU port of [ref] ; with the wormhole campaign of Ref. [ref] these are, to our knowledge, the first evolutions of energy-condition-violating matter in GPU-native numerical relativity, the warp-bubble collapse of Ref. [ref] being the closest CPU-side precedent.
2604.00071 · Introduction · 1.00
Cites as background 1 paper
-
Newtonian $N$-body work has since carried the same sign rules into cosmological structure formation [ref] .
The Bondi universe: Can negative mass drive the cosmological expansion? · Introduction · 0.88
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.