Closed-form deformed incidence relations are constructed for Eguchi-Hanson, self-dual Taub-NUT, and self-dual Plebanski-Demianski spacetimes by resumming the Dunajski-Mason recursion in Plebanski coordinates.
Complex conformal transformations and zero-rest-mass fields
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abstract
We give a simple prescription for relating different solutions to the zero-rest-mass field equations in conformally flat space-time via complex conformal transformations and changes in reality conditions. We give several examples including linearized black holes. In particular, we show that the linearized Plebanski-Demianski and Schwarzschild fields are related by a complex translation and a complex special conformal transformation. Similar results hold for the linearized Kerr and C-metric fields, and for a peculiar toroidal singularity.
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Incidence Relations for Self-Dual Black Holes
Closed-form deformed incidence relations are constructed for Eguchi-Hanson, self-dual Taub-NUT, and self-dual Plebanski-Demianski spacetimes by resumming the Dunajski-Mason recursion in Plebanski coordinates.