Black hole unitarity and antipodal entanglement

TL;DR

This paper proposes that black hole unitarity and antipodal entanglement imply that Hawking radiation is globally pure and entangled across hemispheres, challenging the traditional thermal spectrum view and maintaining consistency with general relativity.

Contribution

It introduces a model where antipodal entanglement ensures unitarity and pure states in black hole evaporation, with a topologically non-trivial spacetime structure.

Findings

Hawking particles are globally entangled across black hole hemispheres.

Unitarity leads to a topologically non-trivial spacetime.

Hawking radiation is locally thermal but globally pure.

Abstract

Hawking particles emitted by a black hole are usually found to have thermal spectra, if not exactly, then by a very good approximation. Here, we argue differently. It was discovered that spherical partial waves of in-going and out-going matter can be described by unitary evolution operators independently, which allows for studies of space-time properties that were not possible before. Unitarity dictates space-time, as seen by a distant observer, to be topologically non-trivial. Consequently, Hawking particles are only locally thermal, but globally not: we explain why Hawking particles emerging from one hemisphere of a black hole must be 100 % entangled with the Hawking particles emerging from the other hemisphere. This produces exclusively pure quantum states evolving in a unitary manner, and removes the interior region for the outside observer, while it still completely agrees locally with the laws of general relativity. Unitarity is a starting point; no other assumptions are made. Region I and the diametrically opposite region II of the Penrose diagram represent antipodal points in a PT or CPT relation, as was suggested before. On the horizon itself, antipodal points are identified. A candidate instanton is proposed to describe the formation and evaporation of virtual black holes of the type described here. Some important explanations and discussion points are added. In the latest of the paper, again some minor inaccuracies are corrected.