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

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.

23 pages, 1 figure. v2: major revision of Section 3.3 (more accurate asymptotics of radial solutions are used), the rest of the text slightly modified, one reference added. v3: Conclusion expanded, 3 references added, minor corrections in the rest of the text, typos corrected

References in corpus (5)

• Heating up an environment around black holes and inside de Sitter space
• Notes on peculiarities of quantum fields in space-times with horizons
• Remarks on the thermofield double state in 4D black hole background
• Quantum evolution of the Hawking state for black holes
• Quantum mechanics of stationary states of particles in a space-time of classical black holes

Cited by in corpus (5)

• Asymptotic behavior of solutions and spectrum of states in the quantum scalar field theory in the Schwarzschild spacetime
• Quantization of spinor field in the Schwarzschild spacetime and spin sums for solutions of the Dirac equation
• Quantization of electromagnetic field in the Schwarzschild spacetime
• Field Quantisations in Schwarzschild Spacetime: Theory versus Low-Energy Experiments
• Peculiarities of quantum field theory in the presence of a wormhole