Quantization of electromagnetic and gravitational perturbations of a Kerr black hole

The electromagnetic and gravitational fluctuations about the classical gravitational field of a rotating black hole are quantized by imposing commutation relations on the Newman-Penrose quantities ${\phi }_0$ and ${\psi }_0$. Two examples which illustrate the utility of the formalism concern the vacuum expectation value of the stress-energy tensor for the electromagnetic field in the Boulware vacuum and the response of an Unruh box coupled to fluctuations of the gravitational field. These quantities are computed in the vicinity of the horizon.