The topological entanglement entropy of black holes in loop quantum gravity

TL;DR

This paper demonstrates that four-dimensional black holes in loop quantum gravity exhibit topological order, characterized by non-zero topological entanglement entropy, affecting their symmetries and the purity of Hawking radiation.

Contribution

It reveals that black holes can have topological order with non-zero entanglement entropy, linking large diffeomorphisms to physical symmetries in quantum gravity.

Findings

Black holes exhibit non-zero topological entanglement entropy.

Large diffeomorphisms act as symmetry transformations.

Hawking radiation can be pure due to topological order.

Abstract

Topological order (long-range entanglement) play important role in modern condensed matter physics. In this paper, we will show that the four dimensional black hole can also have topological order, by showing that the topological entanglement entropy is non-zero. The properties of the topological order show that the large diffeomorphisms will act as symmetry (not gauge) transformation on the physical states. More importantly, the long-range entanglement will make the Hawking radiation pure.