The Bisognano-Wichmann Theorem for Charged States and the Conformal Boundary of a Black Hole

TL;DR

This paper explores the application of Operator Algebras to Quantum Field Theory on curved spacetime, revealing that the incremental entropy of a quantum black hole with added charge is quantized and related to horizon conformal symmetries.

Contribution

It extends the Bisognano-Wichmann theorem to charged states and conformal boundaries of black holes, linking entropy quantization to horizon symmetries.

Findings

Incremental black hole entropy is quantized proportionally to the logarithm of an integer.

Conformal symmetries on the horizon are constructed and utilized.

The approach applies to spacetimes with bifurcate Killing horizons and horizon-localized charges.

Abstract

Recent applications of Operator Algebras to Quantum Field Theory on a Curved Spacetime show that the incremental entropy associated with a quantum black hole, due the addition of a short range charge, is quantized proportionally to the logarithm of an integer. This talk first reviews the case of a Rindler black hole and then sketches the case of a spacetime with bifurcate Killing horizon and charges localizable on the horizon. An important tool is the construction of the conformal symmetries on the horizon.