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arXiv · 2007.09486

The silence of binary Kerr

Rafael Aoude·Ming-Zhi Chung·Yu-tin Huang·Camila S. Machado·Man-Kuan Tam
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Abstract

A non-trivial $\mathcal{S}$-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 $\mathcal{S}$-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 $2\rightarrow 2$ amplitude. In the Eikonal limit, we find that the relative entanglement entropy, defined here as the \textit{difference} between the entanglement entropy of the \textit{in} and \textit{out}-states, is nearly zero for minimal coupling irrespective of the \textit{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.

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Rafael Aoude, Ming-Zhi Chung, Yu-tin Huang, Camila S. Machado, Man-Kuan Tam. 2020-07-18. The silence of binary Kerr. https://doi.org/10.1103/physrevlett.125.181602

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