Proper Field Quantization in Black Hole Spacetimes

TL;DR

This paper revises the understanding of quantum field theory in black hole spacetimes by identifying the true vacuum state as a pure microcanonical state, contrasting with the traditional thermal vacuum.

Contribution

It introduces a microcanonical quantum field theory framework for black holes, providing a more accurate description of particle states and vacuum structure.

Findings

Particles are described by pure states in the microcanonical framework.

The true vacuum differs from the thermal vacuum traditionally used.

Quantum gravity effects imply a non-thermal, pure state description.

Abstract

Canonical quantization of local field theories is classical black hole spacetimes with a single horizon leads to a particle number density with a thermal distribution in equilibrium at the Hawking temperature. A complete treatment including non-local quantum gravity effects has shown however that the full "thermal vacuum" of the theory is the false vacuum. In this work we find the true vacuum consistent with the complete semiclassical analysis of quantum black holes. The theory is described by a "microcanonical" quantum field theory with fixed energy E = M, the mass of the black hole. Considerations making use of the microcanonical density matrix as well as the idempotency condition show that particles in black hole backgrounds are described by pure states, unlike the canonical formulation.