Quasi-Local "Conserved Quantities"

TL;DR

This paper develops a general method for defining quasi-local conserved quantities in gravitating systems with energy flux, using the Noether charge formulation and boundary conditions based on the symplectic structure.

Contribution

It introduces a new prescription for quasi-local conserved quantities that applies to systems with non-zero energy flux, unifying various applications in gravitational physics.

Findings

Consistent definition of energy-momentum and angular momentum at infinity.

Application to asymptotically anti-de Sitter spacetimes.

Insights into thermodynamics of isolated horizons.

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.