Symmetry and entropy of black hole horizons

TL;DR

This paper uses quantum information theory to show that black hole horizon states are constrained by symmetry, linking the Immirzi parameter to entropy and quasi-normal modes in a diffeomorphism-invariant quantum gravity framework.

Contribution

It introduces a novel application of noiseless subsystems to quantum gravity, revealing how symmetries emerge in black hole horizon states and fixing the Immirzi parameter.

Findings

All horizon punctures are equal in the relevant quantum states.

The Immirzi parameter value matches both entropy and quasi-normal mode spectrum.

Symmetries can emerge from diffeomorphism-invariant quantum gravity.

Abstract

We argue, using methods taken from the theory of noiseless subsystems in quantum information theory, that the quantum states associated with a Schwarzchild black hole live in the restricted subspace of the Hilbert space of horizon boundary states in which all punctures are equal. Consequently, one value of the Immirzi parameter matches both the Hawking value for the entropy and the quasi normal mode spectrum of the Schwarzchild black hole. The method of noiseless subsystems thus allows us to understand, in this example and more generally, how symmetries, which take physical states to physical states, can emerge from a diffeomorphism invariant formulation of quantum gravity.