Exploring the Dynamics of General Relativistic Binary-Single and Binary-Binary Encounters of Black Holes

TL;DR

This work demonstrates that the BAM numerical-relativity code can simulate fully relativistic three- and four-body encounters of equal-mass, non-spinning black holes, revealing dynamics and gravitational-wave signals that diverge from post-Newtonian expectations up to $2.5$PN. By employing the moving-puncture method, BSSN evolution, AMR, and careful initial data construction, the authors perform multiple binary-single and binary-binary scattering experiments to map a portion of the high-dimensional parameter space. The results show a spectrum of outcomes—from weak perturbations to chaotic, multi-peak gravitational-wave bursts and complex mergers—highlighting distinctive waveform features and mode-mixing not captured by simpler models. These findings underscore the challenges in detecting and interpreting such exotic, multi-body encounters with current GW search pipelines, while pointing to potential astrophysical relevance in systems formed through hierarchical mergers of supermassive black holes. Overall, the study establishes a framework for detailed relativistic phenomenology of $N$-body BH encounters and motivates future improvements in GW extraction and parameter-space exploration for multi-body GR dynamics.

Abstract

In this exploratory study, we demonstrate the capability of the numerical-relativity code BAM to simulate fully relativistic black-hole binary-single and binary-binary encounters. While previous work has demonstrated the general capability of numerical-relativity frameworks to evolve spacetimes with $N$ black holes, detailed explorations of such encounters remain limited. We focus on scenarios involving initially non-spinning, equal-mass black holes that result in a variety of dynamical outcomes, including flybys, delayed or accelerated eccentric mergers, exchanges, and more complex interactions. Our results show that we can reliably simulate scattering experiments involving three and four black holes, which exhibit interesting dynamics and gravitational-wave signals. The dynamics of these systems show noticeable differences compared to analogous systems in post-Newtonian approximations up to 2.5PN. A key result is that the gravitational waveforms exhibit remarkable features that could potentially make them distinguishable from regular binary mergers.

Figures (24)

• Figure 1: Schematic showing the configuration setup of the black-hole binary-single and binary-binary encounters.
• Figure 2: Left: Three-quarter view of the puncture trajectories of BSS-01a. Right: The same view but without the trajectories of the black holes in the binary and with a strongly rescaled $z$-axis. The trajectory of the single black hole (coming from the right) is colored orange, the trajectory of the center of mass of the binary system (coming from the left) is colored purple, and the trajectories of the binary members are colored blue. The dashed lines and projections indicate the location in 3D space.
• Figure 3: Convergence test for the $z$-component of the binary's center of mass for the configuration BSS-01b.
• Figure 4: Puncture trajectories of the binary members in the setup BSS-01a in their center-of-mass frame, which uses coordinates $u$, $v$ and $w$. The color encodes the positions of the black holes at different times, and the initial positions of the black holes are indicated with black dots. Left: Head-on view of the initial orbital plane. Right: Edge-on view of the initial orbital plane.
• Figure 5: Time evolution of the binary's eccentricity $e_{\mathrm{r}}$ in BSS-01a. The dashed red line marks the time of closest approach of the binary's center of mass and the single black hole.