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, defi…