Complex conformal transformations and zero-rest-mass fields
arXiv:2305.08756 · doi:10.1103/PhysRevD.108.024032
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.
arXiv comment16 pages
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