Seminarium KMMF "Teoria Dwoistości"

Einstein's equations are not conformally invariant, but they exhibit surprising relations to conformal geometry. Many of these conformal properties can be understood using fact that important tensor in conformal geometry, Fefferman-Graham obstruction tensor vanishes on every solution of Einstein gravity. Vanishing of Fefferman-Graham obstruction tensor (Anderson-called Fefferman-Graham equations, AFG) shares many similarities to Einstein's equations for example it is a Lagrangian theory. The problem of charges definition in asymptotically de Sitter spacetimes attracted recently some attention and it is interesting to analyze if AFG equations can be useful also in this context. I will describe relation of Wald-Zoupas charges to AFG equations which touches many interesting results in conformal geometry: for example Alexakis decomposition of global conformal invariants, Yang-Mills currents for conformal normal Cartan connection etc.