Asymptotic behavior of solutions and spectrum of states in the quantum scalar field theory in the Schwarzschild spacetime

Abstract

In this paper, the study of canonical quantization of a free real massive scalar field in the Schwarzschild spacetime is continued. The normalization constants for the eigenfunctions of the corresponding radial equation are calculated, providing the necessary coefficients for the doubly degenerate scatteringlike states that are used in the expansion of the quantum field. It is shown that one can pass to a new type of states such that the spectrum of states with energies larger than the mass of the field splits into two parts. The first part consists of states that resemble properly normalized plane waves far away from the black hole, so they just describe the theory for an observer located in that area. The second part consists of states that live relatively close to the horizon and whose wave functions decrease when one goes away from the black hole. The appearance of the second part of the spectrum, which follows from the initial degeneracy of the scatteringlike states, is a consequence of the topological structure of the Schwarzschild spacetime.

22 pages, 1 figure. v2: minor revision of the text, one reference added, typos corrected

References in corpus (4)

• Heating up an environment around black holes and inside de Sitter space
• Doubling of physical states in the quantum scalar field theory for a remote observer in the Schwarzschild spacetime
• Remarks on the thermofield double state in 4D black hole background
• Quantum mechanics of stationary states of particles in a space-time of classical black holes

Cited by in corpus (3)

• 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
• Peculiarities of quantum field theory in the presence of a wormhole