Silence of Binary Kerr Black Holes

Abstract

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.

Classical Yang-Mills observables from amplitudes

“…Measurement of spin is therefore one of the primary physics outputs of gravitational wave observations. It is fortunate, then, that spin can be incorporated rather naturally in the formalism of quantum field theory [41,76,[90][91][92][93][94][95][96][97][98][99][100][101][102][103][104], even for very large (classical) spins. However the details of spin dynamics quickly becomes complex.…”

Relative entropy in scattering and the S-matrix bootstrap

“…Next, we consider another quantity called Entanglement Power [47][48][49][50]. It deals directly with the S-matrix of the system rather than depending on the initial states.…”

“…Recently, [49,50] explored the entanglement power in the context of S-Matrix evolution. In particular, they used a particular form of p( β 1 ⟩ , β 2 ⟩).…”

Tidal effects for spinning particles

“…A similar analysis to that performed in ref. [67] can be applied to the systems described here, potentially shedding some light on the values of tidal Love numbers for Kerr black holes in a general (but weak) gravitational environment.…”