Binary-induced collapse of a compact, collisionless cluster

TL;DR

This paper models how a relativistic, collisionless cluster around a black hole can undergo gravitational collapse due to the tidal influence of a distant binary companion, extending previous theoretical models.

Contribution

It extends Shapiro's model by incorporating relativistic effects and tidal perturbations to demonstrate collapse in a collisionless cluster near a black hole.

Findings

Tidal fields can induce collapse in relativistic clusters.

The model confirms Bekenstein's conjecture on horizon area invariance.

Relativistic effects are crucial for understanding cluster stability.

Abstract

We improve and extend Shapiro's model of a relativistic, compact object which is stable in isolation but is driven dynamically unstable by the tidal field of a binary companion. Our compact object consists of a dense swarm of test particles moving in randomly-oriented, initially circular, relativistic orbits about a nonrotating black hole. The binary companion is a distant, slowly inspiraling point mass. The tidal field of the companion is treated as a small perturbation on the background Schwarzschild geometry near the hole; the resulting metric is determined by solving the perturbation equations of Regge and Wheeler and Zerilli in the quasi-static limit. The perturbed spacetime supports Bekenstein's conjecture that the horizon area of a near-equilibrium black hole is an adiabatic invariant. We follow the evolution of the system and confirm that gravitational collapse can be induced in a compact collisionless cluster by the tidal field of a binary companion.