Energy-momentum in general relativity

We briefly review of the definitions of the total energy, the total linear momentum and the angular momentum of gravitational field when the cosmological constant is zero. In particular, we show pseudo-tensor’s definition of the energy and the momentum given by Prof. Duan in 1963 agree with the ADM total energy-momentum and the Bondi energy-momentum at spatial and null infinity respectively. We also review the relevant energy-momentum inequalities. Finally, we provide a short review of the positive energy theorem and the peeling property of the Newmann-Penrose quantities when the cosmological constant is positive.