’t Hooft, Gerard The Black hole horizon as a dynamical system. (English) Zbl 1111.83037 Int. J. Mod. Phys. D 15, No. 10, 1587-1602 (2006). Summary: Interactions between outgoing Hawking particles and ingoing matter are determined by gravitational forces and Standard Model interactions. In particular, the gravitational interactions are responsible for the unitarity of the scattering against the horizon, as dictated by the holographic principle, but the Standard Model interactions also contribute, and understanding their effects is an important first step towards a complete understanding of the horizon’s dynamics. The relation between in- and outgoing states is described in terms of an operator algebra. In this contribution, in which earlier results are rederived and elaborated upon, we first describe the algebra induced on the horizon by \(U(1)\) vector fields and scalar fields, including the case of an Englert-Brout-Higgs mechanism, and a more careful consideration of the transverse vector field components. We demonstrate that, unlike classical black holes, the quantized black hole has on its horizon an imprint of its (recent) past history, i.e., quantum hair. The relation between in- and outgoing states depends on this imprint. As a first step towards the inclusion of non-Abelian interactions, we then compute the effects of magnetic monopoles both in the in-states and in the out-states. They completely modify, and indeed simplify, our algebra. Cited in 5 Documents MSC: 83C57 Black holes 83C47 Methods of quantum field theory in general relativity and gravitational theory Keywords:Black hole horizon; area law; operator algebra; eikonal; coordinate shift; quantum hair; Hawking radiation PDFBibTeX XMLCite \textit{G. 't Hooft}, Int. J. Mod. Phys. D 15, No. 10, 1587--1602 (2006; Zbl 1111.83037) Full Text: DOI arXiv References: [1] DOI: 10.1016/0550-3213(85)90418-3 · doi:10.1016/0550-3213(85)90418-3 [2] ’t Hooft G., Class. Quant. Grav. 11 pp 621– [3] ’t Hooft G., Phys. Scripta T 15 pp 143– [4] DOI: 10.1142/S0217751X96002145 · Zbl 1044.81683 · doi:10.1142/S0217751X96002145 [5] DOI: 10.1103/PhysRevLett.23.53 · doi:10.1103/PhysRevLett.23.53 [6] DOI: 10.1088/0264-9381/22/20/001 · Zbl 1084.83024 · doi:10.1088/0264-9381/22/20/001 [7] DOI: 10.1007/BF01206031 · Zbl 0506.76138 · doi:10.1007/BF01206031 [8] ’t Hooft G., World Scientific Series in 20th Century Physics 4, in: Salamfestschrift: A Collection of Talks (1993) [9] DOI: 10.1103/PhysRevD.5.1239 · doi:10.1103/PhysRevD.5.1239 [10] DOI: 10.1146/annurev.ns.07.120157.002203 · doi:10.1146/annurev.ns.07.120157.002203 [11] DOI: 10.1103/PhysRev.115.468 · doi:10.1103/PhysRev.115.468 [12] DOI: 10.1103/PhysRev.135.B1442 · doi:10.1103/PhysRev.135.B1442 [13] DOI: 10.1103/PhysRevLett.13.321 · doi:10.1103/PhysRevLett.13.321 [14] DOI: 10.1016/0031-9163(64)91136-9 · doi:10.1016/0031-9163(64)91136-9 [15] DOI: 10.1103/PhysRevLett.13.508 · doi:10.1103/PhysRevLett.13.508 [16] DOI: 10.1103/PhysRev.145.1156 · doi:10.1103/PhysRev.145.1156 [17] DOI: 10.1016/0550-3213(81)90442-9 · doi:10.1016/0550-3213(81)90442-9 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.