Quantization of a charged scalar field on a charged black hole background

TL;DR

This paper develops quantum states for a charged scalar field around a charged black hole, extending standard neutral field states and analyzing their physical properties and differences.

Contribution

It introduces new charged black hole quantum states analogous to Boulware, Unruh, and Hartle-Hawking states, using nonstandard commutation relations for superradiant modes.

Findings

Constructed charged black hole quantum states with physical properties similar to neutral cases.

Computed expectation value differences of field condensate, current, and stress-energy tensor.

Presented tentative equilibrium states including a Boulware-like and a Hartle-Hawking-like state.

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.