Eur. Phys. J. Plus (2020) 135: 104
https://doi.org/10.1140/epjp/s13360-020-00157-6

Regular Article

Gravitational slingshots around black holes in a binary

¹ Gravitational Wave and Cosmology Laboratory, Department of Astronomy, Beijing Normal University, Beijing, 100875, China
² Department of Physics and Astronomy, West Virginia University, PO Box 6315, Morgantown, WV, 26506, USA

^* e-mail: fnzhang@bnu.edu.cn

Received: 20 May 2019
Accepted: 14 November 2019
Published online: 23 January 2020

Abstract

The speed gain of a test mass from taking a gravitational slingshot around a celestial object (scattering centre) increases with the latter’s speed and compactness (stronger deflection of the mass’ trajectory becomes possible without it hitting the surface of the object). The black holes (BHs) in a tight binary (consisting of two black holes; we are not considering X-ray binaries), themselves moving at relativistic speeds, represent optimal scattering centres. Therefore, a subpopulation of accreting matter particles, swept up into chaotic orbits around a BH binary, might repeatedly take slingshots and become accelerated to ultra-relativistic speeds (as seen by observers on Earth), ultimately escaping from the binary, as well as the fate of being devoured by a BH. The escaped particles can plausibly be observed on Earth as ultra-high-energy cosmic rays. Investigating such a possibility would require general relativistic slingshot formulae due to the high speeds involved and the close encounters with BHs. We derive them in this paper and show that the percentage gain per slingshot in a particle’s Lorentz factor remains undiminished even as the particle energizes up, thus demonstrating that the slingshot mechanism can in principle accelerate particles to extreme energies.