Binary Ellis-Bronnikov wormholes in 3+1 numerical relativity: mergers, fly-bys and gravitational waves

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 $1.462\pm0.022$ 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.