Conformal Yano-Killing tensors and asymptotic CYK tensors for the Schwarzschild metric

We show some general properties of the conformal Yano-Killing tensor on a Riemannian manifold. Several differential and algebraic equations are derived. The asymptotic conformal Yano-Killing tensor proposed earlier by the author is analysed for the Schwarzschild metric and the tensor equations defining this object are given. The result shows that the Schwarzschild metric (and other metrics which are asymptotically 'Schwarzschildean' up to O(1/r(2)) at spatial infinity) is among the metrics fulfilling stronger asymptotic conditions and supertranslation ambiguities disappear. It is also clear from the result that 14 asymptotic gravitational charges are well defined on the 'Schwarzschildean' background.