Symmetry and entropy of black hole horizons Original Research Article

We argue, using methods taken from the theory of noiseless subsystems in quantum information theory, that the quantum states associated with a Schwarzschild 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 Schwarzschild black hole. The method of noiseless subsystems 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.