Hertz potentials in higher dimensions

Abstract

The author generalises the Hertz potentials to all spacetime dimensions D>or=4 and to all antisymmetric tensor fields. He shows that the Whittaker-Debye-Bromwich reduction of the Hertz potential can be successfully exploited in all dimensions and for all antisymmetric tensor fields if the underlying spacetime is a warped product manifold. He illustrates the Hertzian approach by constructing the multipole expansions of all antisymmetric tensor fields on a D-dimensional Schwarzschild solution. A no-hair theorem for the D-dimensional black holes follows from these multipole expansions.