Binary-induced collapse of a compact, collisionless cluster - art. no. 104024

We improve and extend Shapiro's model of a relativistic, compact object whi ch is stable in isolation but is driven dynamically unstable by the tidal f ield of a binary companion. Our compact object consists of a dense swarm of test particles moving in randomly oriented, initially circular, relativist ic orbits about a nonrotating black hole. The binary companion is a distant , slowly inspiraling point mass. The tidal field of the companion is treate d as a small perturbation on the background Schwarzschild geometry near the hole; the resulting metric is determined by solving the perturbation equat ions of Regge and Wheeler and Zerilli in the quasi-static limit. The pertur bed spacetime supports Bekenstein's conjecture that the horizon area of a n ear-equilibrium black hole is an adiabatic invariant. We follow the evoluti on of the system and confirm that gravitational collapse can be induced in a compact collisionless cluster by the tidal field of a binary companion. [ S0556-2821(99)00720-1].