ÃÛÌÒTV

Due to the geometric structure of the Kerr solution, test fields on such a background have special properties such as decoupling, symmetry or separability. A covariant characterization of these properties in terms of a Killing spinor will be presented. In particular the dynamics of the linearized gravitational field is governed by certain curvature components solving the Teukolsky master equations (TME) and Teukolsky-Starobinski identities (TSI). I will show that the TME and TSI operators are self-adjoint in an appropriate sense. Combined with an adjoint operator argument due to Wald, this leads to symmetry operators of the linearized Einstein equations of order four and six, respectively. Interpretations and possible applications will be discussed. The results were derived using 2-spinors and advanced symbolic computer algebra tools for xAct, which I will introduce briefly.