Conserved Charges in General Relativity: Energy and Gravitational Charge

General relativity is constructed based on two fundamental principles: general covariance and the equivalence principle. However, defining "energy conservation" itself is nontrivial in curved spacetime. Various definitions such as Einstein's pseudo-tensor, Komar energy, and ADM energy have been proposed, but their physical meanings have not been clear.

In this talk, we apply the post-Newtonian approximation to a system of massive particles interacting only through gravity, and clarify what physical quantities each conserved charge represents. Furthermore, we show that there exists a new conserved charge (gravitational charge) independent of energy, which corresponds to the particle number in this system.