Non-orbital particle trapping in binary black holes through dynamic stability

We present an interdisciplinary comparison between binary black hole systems and Radio Frequency (RF) Paul Traps, modeling the gravitational binary system as a rotating saddle near its center. This analogy connects these seemingly unrelated systems through the concept of dynamic stability. The rotating saddle potential is analytically tractable, allowing us to prove the existence of bounded charged particle trajectories under certain conditions. By focusing on stellar-mass black holes with a weak electric charge-a feature consistent with specific astrophysical conditions that leaves the spacetime metric largely unaffected but can influence nearby particle interactions-we can neglect complicating factors such as magnetic fields from large accretion disks of heavier black holes or stellar winds. Our simulation results demonstrate that charged particles can exhibit stable, non-orbital trajectories near the center of a binary system with charged stellar-mass black holes, providing unique three-dimensional trapping primarily through gravity. This system is distinctive in the literature for its non-orbital trapping mechanism. While theoretically intriguing, this trapping relies on specific conditions, including nearly identical black hole masses. These types of non-orbital trapping mechanisms could potentially allow for longer-lived plasma configurations, enhancing our ability to detect electromagnetic signatures from these systems. The significance of this work lies in the novel comparison between a laboratory-scale quantum system and a larger astrophysical one, opening new avenues for exploring parallels between microscopic and cosmic phenomena across fourteen orders of magnitude in distance.