The Bondi dipole in full numerical relativity: a self-accelerating positive-negative mass binary
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.
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BibTeX
@misc{shirokov2026bondi,
title = {{The Bondi dipole in full numerical relativity: a self-accelerating positive-negative mass binary}},
author = {Nikita M. Shirokov and Ilya Nachevsky},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.24577},
eprint = {2608.24577},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.24577},
}
RIS
TY - UNPB
TI - The Bondi dipole in full numerical relativity: a self-accelerating positive-negative mass binary
AU - Nikita M. Shirokov
AU - Ilya Nachevsky
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2608.24577
UR - https://arxiv.org/abs/2608.24577
AB - 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.
ER -