Nonexistence of time-periodic solutions of the Dirac equation in an axisymmetric black hole geometry

摘要

We prove that in the nonextreme Kerr-Newman black hole geometry, the Dirac equation has no normalizable, time-periodic solutions. A key tool is Chandrasekhar's separation of the Dirac equation in this geometry. A similar nonexistence theorem is established in a more general class of stationary, axisymmetric metrics in which the Dirac equation is known to be separable. These results indicate that, in contrast: to the classical situation of massive particle orbits, a quantum mechanical Dirac particle must either disappear into the black hole or escape to infinity. (C) 2000 John Wiley & Sons, Inc. [References: 19]