Séminaire de Mathématique

# From operator identities to symmetry operators

## by Prof. Steffen AKSTEINER (Potsdam)

Europe/Paris
Amphithéâtre Léon Motchane (IHES)

### Amphithéâtre Léon Motchane

#### IHES

Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
Description

Séminaire de Relativité Générale Mathématique

The hidden symmetry of the Kerr spacetime, encoded in its pair of conformal Killing-Yano tensors, implies hidden symmetries for various test fields on such a background. Starting from certain natural operator identities we derive two such symmetries of the linearized Einstein operator. The first one is of differential order four and the relation to the classical theory of Debye potentials as well as to the Chandrasekhar transformation will be explained. The second one is of differential order six and related to the separability of an integrability condition to the linearized Einstein equations — the Teukolsky equation. Advanced symbolic computer algebra tools for xAct were developed for this purpose and if time permits, I will give an overview on the current status.

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