The silence of binary Kerr
Abstract
A non-trivial S-matrix generally implies a production of entanglement: starting with an incoming pure state the scattering generally returns an outgoing state with non-vanishing entanglement entropy. It is then interesting to ask if there exists a non-trivial S-matrix that generates no entanglement. In this letter, we argue that the answer is the scattering of classical black holes. We study the spin-entanglement in the scattering of arbitrary spinning particles. Augmented 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 non-vanishing spin multipole moments. This suggests that minimal couplings of spinning particles, whose classical limit corresponds to Kerr black hole, has the unique feature of generating near zero entanglement.