Twistor theory and the Teukolsky equations

BERNARDO ARANEDA

Estocolmo

Encuentro; General Relativity, Geometry and Analysis: Beyond the first 100 years after Einstein; 2019

Institut Mittag-Leffler

The Teukolsky equations are currently the leading approach for the analysis of linear stability of black holes. They involve a complicated differential operator and can be obtained from the field equations by quite tricky procedures, but some results in the literature suggest that there could be an interesting geometric structure underlying them. On the other hand, Penrose's twistor theory is an approach to fundamental physics where spacetime is secondary to the more primitive twistor space, which is a 3-dimensional complex manifold whose points correspond to certain surfaces in the spacetime. We will show that the geometry of the Teukolsky equations can be naturally understood by considering 2-dimensional twistor spaces, and as by-products we will show the appearance of (generalized) hidden symmetries, Hertz potentials, symmetry operators, and conformal and complex structures.