Two-dimensional twistor manifolds and Teukolsky operators
arXiv:1907.02507 · doi:10.1007/s11005-020-01307-8
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.
arXiv comment28 pages. V2: references added; expanded discussion on complex and holomorphic structures; one section added; minor changes in notation. The term `twistor surface' was replaced by `2D twistor space' in order to avoid possible confusion with other twistor concepts
References in corpus (14)
- Perturbative Gauge Theory As A String Theory In Twistor Space
- Black holes, hidden symmetries, and complete integrability
- New identities for linearized gravity on the Kerr spacetime
- Four--Dimensional Metrics Conformal to Kahler
- Teukolsky Master Equation: De Rham wave equation for the gravitational and electromagnetic fields in vacuum
- Linearized gravity and gauge conditions
- Second order symmetry operators
- Anti-self-dual conformal structures with null Killing vectors from projective structures
- The Calabi complex and Killing sheaf cohomology
- Canonical Energy and Hertz Potentials for Perturbations of Schwarzschild Spacetime
- Symmetry operators and decoupled equations for linear fields on black hole spacetimes
- Conformal invariance, complex structures, and the Teukolsky connection
- The Goldberg-Sachs theorem in linearized gravity
- Generalized wave operators, weighted Killing fields, and perturbations of higher dimensional spacetimes