A QFT information protocol for charged black holes

TL;DR

This paper extends quantum information retrieval protocols to charged black holes within Quantum Field Theory, linking algebraic structures to thermodynamics and charge quantization during black hole evaporation.

Contribution

It generalizes existing protocols to type III von Neumann algebras, providing a thermodynamic interpretation and insights into charge quantization in black hole evaporation.

Findings

Derived a formula relating superselection sectors to black hole charge evaporation.

Connected the statistical dimension to thermodynamic properties of black holes.

Identified a quantization constraint on emitted black hole charge.

Abstract

A generalization for the quantum information retrieval protocol recently illustrated by Verlinde and van der Heijden for evaporating black holes is provided to inclusions of type III von Neumann factors. The physical interest of such scenario arises in Quantum Field Theory, where local algebras are type III von Neumann algebras. The formula obtained can be easily interpreted in terms of the statistical dimension of superselection sectors in the case of black holes undergoing charge evaporation, thanks to the index-statistics theorem, leading to a thermodynamic interpretation. A constraint on the values of the index leads to a final remark about the quantization of the charge emitted by the black hole during the evaporation process.