Twistor quadrics and black holes

TL;DR

This paper presents a method to construct curved, non-self-dual Kaehler metrics on space-time using deformations of holomorphic quadrics in twistor space, deriving notable black hole solutions like Schwarzschild and Kerr.

Contribution

It introduces a new procedure linking twistor geometry to physically relevant black hole space-times through specific metric deformations.

Findings

Derived Schwarzschild, Kerr, and Plebanski-Demianski space-times from twistor deformations.

Provided a systematic way to construct non-self-dual Kaehler metrics in space-time.

Connected twistor geometry with classical black hole solutions.

Abstract

A simple procedure is given to construct curved, non-self-dual (complexified) Kaehler metrics on space-time in terms of deformations of holomorphic quadric surfaces in flat twistor space. Imposing Lorentzian reality conditions, the Schwarzschild, Kerr, and Plebanski-Demianski space-times (among others) are derived as examples of the construction.