Conformal Yano-Killing Tensors in General Relativity

How CYK tensors appear in General Relativity? - Geometric definition of the asymptotic flat spacetime: strong asymptotic flatness, which guarantees well defined total angular momentum; - Conserved quantities - asymptotic charges; - Quasi-local mass and 'rotational energy' for Kerr black hole; - Constants of motion along geodesics and symmetric Killing tensors; Spacetimes possessing CYK tensor: - Minkowski (quadratic polynomials); - (Anti-)deSitter (natural construction); - Kerr (type D spacetime); - Taub-NUT (new symmetric conformal Killing tensors); Other applications: - Symmetries of Dirac operator; - Symmetries of Maxwell equations.