Spontaneous excitation of a static multilevel atom coupled with electromagnetic vacuum fluctuations in Schwarzschild spacetime

We study the spontaneous excitation of a radially polarized static multilevel atom outside a spherically symmetric black hole in multi-polar interaction with quantum electromagnetic fluctuations in the Boulware, Unruh and Hartle-Hawking vacuum states. We find that spontaneous excitation does not occur in the Boulware vacuum, and, in contrast to the scalar field case, spontaneous emission rate is not well-behaved at the event horizon as result of the blow-up of the proper acceleration of the static atom. However, spontaneous excitation can take place both in the Unruh and the Hartle-Hawking vacua as if there were thermal radiation from the black hole. Distinctive features in contrast to the scalar field case are the existence of a term proportional to the proper acceleration squared in the rate of change of the mean atomic energy in the Unruh and the Hartle-Hawking vacuums and the structural similarity in the spontaneous excitation rate between the static atoms outside a black hole and uniformly accelerated ones in a flat space with a reflecting boundary, which is particularly dramatic at the event horizon where a complete equivalence exists.