Quasi-Local "Conserved Quantities"

Abstract

Using the Noether Charge formulation, we study a perturbation of the conserved gravitating system. By requiring the boundary term in the variation of the Hamiltonian to depend only on the symplectic structure, we propose a general prescription for defining quasi-local ``conserved quantities'' (i.e. in the situation when the gravitating system has a non-vanishing energy flux). Applications include energy-momentum and angular momentum at spatial and null infinity, asymptotically anti-deSitter spacetimes, and thermodynamics of the isolated horizons.