Black Hole Mergers and Unstable Circular Orbits

TL;DR

This paper investigates the dynamics of black hole mergers near the threshold of immediate merger, revealing a near-circular orbit phase and an analogy with unstable geodesics, with implications for high-energy particle collisions.

Contribution

It introduces a detailed numerical study of black hole merger thresholds and draws an analogy with geodesic behavior, offering new insights into black hole scattering and potential collider applications.

Findings

Near-threshold binary black holes exhibit a whirl phase similar to unstable geodesics.

Scaling exponents for whirl phases are comparable between binary mergers and geodesic orbits.

The study provides estimates for black hole scattering cross sections and energy emissions.

Abstract

We describe recent numerical simulations of the merger of a class of equal mass, non-spinning, eccentric binary black hole systems in general relativity. We show that with appropriate fine-tuning of the initial conditions to a region of parameter space we denote the threshold of immediate merger, the binary enters a phase of close interaction in a near-circular orbit, stays there for an amount of time proportional to logarithmic distance from the threshold in parameter space, then either separates or merges to form a single Kerr black hole. To gain a better understanding of this phenomena we study an analogous problem in the evolution of equatorial geodesics about a central Kerr black hole. A similar threshold of capture exists for appropriate classes of initial conditions, and tuning to threshold the geodesics approach one of the unstable circular geodesics of the Kerr spacetime. Remarkably, with a natural mapping of the parameters of the geodesic to that of the equal mass system, the scaling exponent describing the whirl phase of each system turns out to be quite similar. Armed with this lone piece of evidence that an approximate correspondence might exist between near-threshold evolution of geodesics and generic binary mergers, we illustrate how this information can be used to estimate the cross section and energy emitted in the ultra relativistic black hole scattering problem. This could eventually be of use in providing estimates for the related problem of parton collisions at the Large Hadron Collider in extra dimension scenarios where black holes are produced.