Quantization of electromagnetic field in the Schwarzschild spacetime

TL;DR

This paper develops a consistent method for quantizing the electromagnetic field in Schwarzschild spacetime, avoiding the black hole's interior, and introduces a unitary gauge compatible with the field equations.

Contribution

It presents a novel canonical quantization procedure for electromagnetic fields in Schwarzschild spacetime, including a new unitary gauge and analysis of stationary states.

Findings

Existence of a unitary gauge combining Coulomb and Poincare gauges

Canonical commutation relations derived for the quantized field

Hamiltonian formulation of the electromagnetic field in this spacetime

Abstract

We discuss the problem of canonical quantization of electromagnetic 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 internal region of the black hole. We prove that there exists a unitary gauge, which can be viewed as a combination of the Coulomb and Poincare gauges and is compatible with the field equations. The solutions corresponding to the stationary one-particle states of the electromagnetic field are studied, the canonical commutation relations and the Hamiltonian of the quantized electromagnetic field are obtained.