Binary-Induced Gravitational Collapse: A Trivial Example

We present a simple model illustrating how a highly relativistic, compact object which is stable in isolation can be driven dynamically unstable by the tidal field of a binary companion. Our compact object consists of a test-particle in a relativistic orbit about a black hole; the binary companion is a distant point mass. Our example is presented in light of mounting theoretical opposition to the possibility that sufficiently massive, binary neutron stars inspiraling from large distance can collapse to form black holes prior to merger. Our strong-field model suggests that first order post-Newtonian treatments of binaries, and stability analyses of binary equilibria based on orbit-averaged, mean gravitational fields, may not be adequate to rule out this possibility.