Kaehler geometry of black holes and gravitational instantons

Abstract

We obtain a closed formula for the Kaehler potential of a broad class of four-dimensional Lorentzian or Euclidean conformal "Kaehler" geometries, including the Plebanski-Demianski class and various gravitational instantons such as Fubini-Study and Chen-Teo. We show that the Kaehler potentials of Schwarzschild and Kerr are related by a Newman-Janis shift. Our method also shows that a class of supergravity black holes, including the Kerr-Sen spacetime, is Hermitian (but not conformal Kaehler). We finally show that the integrability conditions of complex structures lead naturally to the (non-linear) Weyl double copy, and we give new vacuum and non-vacuum examples of this relation.

6 pages

References in corpus (5)

• Black holes and the double copy
• A worldsheet for Kerr
• The SAGEX Review on Scattering Amplitudes
• Zero mass limit of Kerr spacetime is a wormhole
• A five-parameter class of solutions to the vacuum Einstein equations

Cited by in corpus (3)

• Complex degenerate metrics in general relativity: a covariant extension of the Moore-Penrose algorithm
• Complex conformal transformations and zero-rest-mass fields
• Newman-Janis Algorithm from Taub-NUT Instantons