Complementarity and the unitarity of the black hole S-matrix

• Published in: The journal of high energy physics Vol. 2023; no. 2; pp. 233 - 46
• Main Authors: Kim, Isaac H., Preskill, John
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 24.02.2023; Springer Nature B.V; Springer Nature; SpringerOpen
• Subjects: Black Holes; Classical and Quantum Gravitation; Complexity; Elementary Particles; Entropy; High energy physics; Holography; Models of Quantum Gravity; Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Polynomials; Principles; Pseudorandom; Quantum computing; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Radiation; Regular Article - Theoretical Physics; Relativity Theory; S matrix theory; String Theory; Black Holes; Models of Quantum Gravity
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP02(2023)233

A bstract Recently, Akers et al. proposed a non-isometric holographic map from the interior of a black hole to its exterior. Within this model, we study properties of the black hole S -matrix, which are in principle accessible to observers who stay outside the black hole. Specifically, we investigate a scenario in which an infalling agent interacts with radiation both outside and inside the black hole. Because the holographic map involves postselection, the unitarity of the S -matrix is not guaranteed in this scenario, but we find that unitarity is satisfied to very high precision if suitable conditions are met. If the internal black hole dynamics is described by a pseudorandom unitary transformation, and if the operations performed by the infaller have computational complexity scaling polynomially with the black hole entropy, then the S -matrix is unitary up to corrections that are superpolynomially small in the black hole entropy. Furthermore, while in principle quantum computation assisted by postselection can be very powerful, we find under similar assumptions that the S -matrix of an evaporating black hole has polynomial computational complexity.