Covariant Energy-Momentum Conservation in General Relativity with Cosmological Constant

Abstract

A covariant formula for conserved currents of energy, momentum and angular-momentum is derived from a general form of Noether’s theorem applied directly to the Einstein-Hilbert action of classical general relativity. Energy conservation in closed and flat big-bang cosmologies including cosmic radiation and dark energy is discussed as special cases.  Special care is taken to distinguish between kinematic and dynamic expressions.