Quasi-local instant charges and its asymptotics at spatial infinity

We provide a new construction of charges (conserved quantities) for the gravity field in the (3+1) decomposition. The construction is based on (3+1) splitting of conformal Yano--Killing tensor. We obtain charges, defined on Cauchy surface, which are combined from components of Weyl tensor and conformal Killing vector. The relations between the conserved quantities and its classical ADM counterparts are revisited. Asymptotic behavior of the conserved quantities is described. The charges are analyzed for a particular choice of initial data, among others, Bowen--York spinning black hole.