Detecting relativistic black hole collisions near a massive black hole

TL;DR

This work investigates relativistic black-hole collisions occurring in a massive black-hole background, modeling two equal-mass, spinless BHs boosted by a Kerr MBH and their mutual attraction. It employs the CLAP framework with the Zerilli equation and Misner initial data, incorporating initial-boost corrections to generate gravitational-wave waveforms and applying redshift to observables. The study finds achievable boosts up to $P/m_0 \approx 1.4$ after two acceleration stages and shows that the dominant $(2,0)$ mode governs the emission, with higher multipoles remaining subdominant for modest boosts. Detection prospects are mapped across TianQin, LISA (and Taiji), CE, ET, and LIGO, revealing strong horizons for space-based detectors (up to redshifts $z \sim 9$–$16$) and meaningful but more limited reach for ground-based detectors, alongside promising parameter-estimation capabilities that motivate further exploration of more general collision scenarios in MBH environments.

Abstract

Relativistic black hole collisions are one of the most dramatic astrophysical events that can be imagined. They could provide the ideal condition for searching for possible new physics beyond general relativity. However, such events are presumably rare and difficult to occur under normal conditions. Black holes in a triple system can be accelerated to the relativistic limit and may harbor the chance for a relativistic collision. In this paper, we study the relativistic black hole collisions in a massive black hole background and the capabilities of several current and future gravitational wave detectors in detecting such signals.

Figures (13)

• Figure 1: The closest periastron for marginally stable elliptical orbits, varing with eccentricity and the specific angular momentum of the background MBH. Note $a<0$ corresponds to retrograde orbits and $a>0$ corresponds to prograde orbits.
• Figure 2: The periastron radius of parabolic orbits around Kerr black holes. The black curve denotes the closest periastron for all possible values of $L$, and the other colored curves denote orbits with various fixed values of $L$. Note $a<0$ corresponds to retrograde trajectories and $a>0$ corresponds to prograde trajectories.
• Figure 3: An illustration of the detection scenario considered in this paper.
• Figure 4: Waveform numerically calculated for two different values of initial boost, as observed by an observer fixed at $r = 200m$.
• Figure 5: A comparison of the radiated energy of the (2,0), (4,0) and (6,0) modes.