Seminarium KMMF "Teoria Dwoistości"

Properties of (skew-symmetric) conformal Yano--Killing tensors are reviewed. The examples of CYK tensors in Minkowski, Kerr, de Sitter and anti-de Sitter spacetimes are discussed.Basic facts and definitions of the spin--2 field and conformal Yano-Killing tensors are introduced.Application of those two objects provides a precise definition of quasi-local gravitational charge.It leads to geometric definition of the asymptotic flat spacetime:`strong asymptotic flatness',which guarantees well defined total angular momentum.Conformal rescaling of conformal Yano--Killing tensors and relations between Yano and CYK tensors are discussed.Pullback of these objects to a submanifold is used to construct all solutions of a CYK equation in anti-de Sitter and de Sitterspacetimes.Properties of asymptotic conformal Yano--Killing tensors are examined for asymptotic anti-de Sitter spacetimes. Explicit asymptotic forms of them are derived. The results are used to construct asymptotic chargesin asymptotic AdS spacetime. Well known examples like Schwarzschild-AdS, Kerr-AdS and NUT-AdS are examined carefully in the construction of the concept of energy, angular momentum and dual mass in asymptotic AdS spacetime.Other applications: symmetric Killing tensors and constants of motion along geodesics.