Energy-Momentum Conservation in General Relativity

Abstract

We discuss general properties of the conservation law associated with a local symmetry. Using Noether's theorem and a generalized Belinfante symmetrization procedure in 3+1 dimensions, a symmetric energy-momentum (pseudo) tensor for the gravitational Einstein-Hilbert action is derived and discussed in detail. In 2+1 dimensions, expressions are obtained for energy and angular momentum arising in the $ISO(2,1)$ gauge theoretical formulation of Einstein gravity. In addition, an expression for energy in a gauge theoretical formulation of the string-inspired 1+1 dimensional gravity is derived and compared with the ADM definition of energy.

18 pages in Plain TeX, MIT-CTP-2245

References in corpus (7)

• Black Hole Entropy is Noether Charge
• Evanescent Black Holes
• Gauge Invariant Formulations of Lineal Gravity
• Poincaré Gauge Theory for Gravitational Forces in (1+1) Dimensions
• Hamiltonian Approach to 2D Dilaton-Gravities and Invariant Adm Mass
• Geometric Gravitational Forces on Particles Moving in a Line
• Two Dimensional Quantum Dilaton Gravity and the Positivity of Energy

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