# Two-dimensional twistor manifolds and Teukolsky operators

## TL;DR

This paper explores the connection between Teukolsky equations for black hole stability and twistor theory, revealing that a 2-dimensional twistor manifold underpins the geometric structures involved.

## Contribution

It demonstrates that the geometric structures of Teukolsky equations can be naturally understood through a 2-dimensional twistor manifold, extending twistor theory insights.

## Key findings

- Teukolsky equations relate to a 2D twistor manifold.
- Geometric structures of black hole perturbations are explained via twistor theory.
- A new perspective on the underlying geometry of Teukolsky equations is provided.

## Abstract

The Teukolsky equations are currently the leading approach for analysing stability of linear massless fields propagating in rotating black holes. It has recently been shown that the geometry of these equations can be understood in terms of a connection constructed from the conformal and complex structure of Petrov type D spaces. Since the study of linear massless fields by a combination of conformal, complex and spinor methods is a distinctive feature of twistor theory, and since versions of the twistor equation have recently been shown to appear in the Teukolsky equations, this raises the question of whether there are deeper twistor structures underlying this geometry. In this work we show that all these geometric structures can be understood naturally by considering a {\em 2-dimensional} twistor manifold, whereas in twistor theory the standard (projective) twistor space is 3-dimensional.