Silence of Binary Kerr Black Holes

A nontrivial S matrix generally implies a production of entanglement: starting with an incoming pure state, the scattering generally returns an outgoing state with nonvanishing entanglement entropy. It is then interesting to ask if there exists a nontrivial S matrix that generates no entanglement. In this Letter, we argue that the answer is the S-matrix for the scattering of classical black holes. We study the spin entanglement in the scattering of arbitrary spinning particles. Augmenting the S-matrix with Thomas-Wigner rotation factors, we derive the entanglement entropy from the gravitational induced 2→2 amplitude. In the Eikonal limit, we find that the relative entanglement entropy, defined here as the difference between the entanglement entropy of the in and out states, is nearly zero for minimal coupling irrespective of the in state and increases significantly for any nonvanishing spin multipole moments. This finding suggests that minimal couplings of spinning particles, whose classical limit corresponds to a Kerr black hole, have the unique feature of generating near zero entanglement.