The black hole horizon as a dynamical system

TL;DR

This paper explores the quantum dynamics of black hole horizons, focusing on how Standard Model interactions and magnetic monopoles influence the horizon's operator algebra and encode the black hole's recent history.

Contribution

It extends previous work by analyzing the horizon algebra with U(1) fields, including the Higgs mechanism, and incorporates magnetic monopoles to understand their impact on horizon dynamics.

Findings

Quantized black holes exhibit quantum hair reflecting recent history.

Inclusion of magnetic monopoles simplifies the horizon algebra.

Horizon operator algebra is influenced by Standard Model interactions.

Abstract

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.