Doubling of physical states in the quantum scalar field theory for a remote observer in the Schwarzschild spacetime

TL;DR

This paper investigates the canonical quantization of a scalar field in Schwarzschild spacetime, revealing a novel doubling of quantum states observable at a distance, due to the spacetime's topology.

Contribution

It introduces a quantization approach using scattering states instead of spherical harmonics, uncovering a topological doubling of quantum states in black hole spacetime.

Findings

Quantum states double for distant observers

Doubling is a topological effect independent of observer position

Standard Hamiltonian form is preserved in the quantization

Abstract

We discuss the problem of canonical quantization of a free real massive scalar field in the Schwarzschild spacetime. It is shown that a consistent procedure of canonical quantization of the field can be carried out without taking into account the black hole interior, so that in the resulting theory the canonical commutation relations are satisfied exactly, and the Hamiltonian has the standard form. However, unlike some papers, in which the expansion of the quantum field in spherical harmonics is used, here we use an expansion in scatteringlike states for energies larger than the mass of the field. This reveals a strange property of the resulting quantum field theory - doubling of the quantum states, which look as having the same asymptotic momentum to an observer located far away from the black hole. This purely topological effect cannot be eliminated by moving away from the black hole.