Local black holes are typeD on the Horizon

Abstract

For the most general static and axisymmetric local black hole with (topologically) spherical or toroidal horizon we calculate the Riemann tensor, we construct a Newman-Penrose null tetrad, we evaluate Weyl scalars and we investigate the algebraic type of the solutions. We find that the spherical black holes are of Petrov typeD on the horizon and on the axis of azimuthal symmetry, while the toroidal ones are of typeD on the horizon and on the plane of the reflectional symmetry.