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Covariant Energy-Momentum Conservation in General Relativity with Cosmological Constant

Philip Gibbs-2010-08-01
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TL;DRAbstract

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.

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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.

Keywords

Noether's theoremPhysicsCovariant transformationIntroduction to the mathematics of general relativityGeneral relativityClassical mechanicsEnergy–momentum relationFour-force

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