Quantization of a charged scalar field on a charged black hole background
arXiv:2205.14483 · doi:10.1103/PhysRevD.106.125013
Abstract
We study the canonical quantization of a massless charged scalar field on a Reissner-Nordstrom black hole background. Our aim is to construct analogues of the standard Boulware, Unruh and Hartle-Hawking quantum states which can be defined for a neutral scalar field, and to explore their physical properties by computing differences in expectation values of the scalar field condensate, current and stress-energy tensor operators between two quantum states. Each of these three states has a non-time-reversal-invariant ``past'' and ``future'' charged field generalization, whose properties are similar to those of the corresponding ``past'' and ``future'' states for a neutral scalar field on a Kerr black hole. In addition, we present some tentative, time-reversal-invariant, equilibrium states. The first is a ``Boulware''-like state which is as empty as possible at both future and past null infinity. Second, we posit a ``Hartle-Hawking''-like state which may correspond to a thermal distribution of particles. The construction of both these latter states relies on the use of nonstandard commutation relations for the creation and annihilation operators pertaining to superradiant modes.
arXiv comment48 pages, 12 figures, minor changes, accepted for publication
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