Quantization of a scalar field in the Kerr spacetime

Abstract

The interaction of a scalar field with the Kerr gravitational field is studied. The properties of the Klein--Gordon equation in the Kerr metric are reviewed, and a two-component formalism is developed. This formalism expresses the one-particle quantum theory for a massive scalar particle in the Kerr metric. A semiclassical analysis of the spontaneous emission of particles by a Kerr black hole is given. The quantization of a scalar field in the Kerr metric is developed, and a treatment of the spontaneous particle creation is given. The particular quantization given here leads to emission only into the classical superradiant modes and hence no emission by a Schwarzschild black hole. In the case in which $omega$M is very much less than 1, where M is the mass of the black hole and $omega$ is the frequency of a given mode, an explicit expression may be given for the rate at which particles are emitted into each mode. In the case in which the particle's mass is zero and a is very much less than M, a = angular momentum per unit mass of the black hole, the total rate of loss of energy of the black hole is shown to be proportionalmore » to a$sup 6$/M$sup 8$. A discussion of the problem of the vacuum energy is given. It is shown that the energy of the vacuum state of a scalar field in a Kerr spacetime a very-much-less-than M is the same as that for a Schwarzschild (a = 0) spacetime. (AIP)« less