A homogeneous Hilbert problem for the Kinnersley–Chitre transformations

Abstract

A homogeneous Hilbert (Riemann) problem (HHP) is introduced for carrying out the Kinnersley–Chitre transformations of the set V of all axially symmetric stationary vacuum spacetimes, and the spacetimes which are like the axially symmetric stationary ones except that both Killing vectors are spacelike. A proof, which is independent of the Kinnersley–Chitre formalism, establishes that the HHP transforms the potential (for certain closed self‐dual 2 forms) F₀(x, t) of any given member of V into the potential F (x, t) of another member of V. Two illustrative examples involving the Minkowski space F₀(x, t) are given. The representation used for the Geroch group K, the singularities and gauge of the potentials, and possible applications of the HHP are discussed.