Energy-Momentum Conservation in General Relativity
Dongsu Bak, D. Cangemi, and R. Jackiw
TL;DR
This paper explores the properties of conservation laws in general relativity, deriving symmetric energy-momentum tensors using Noether's theorem and applying these to various dimensions and formulations.
Contribution
It introduces a generalized Belinfante symmetrization for the energy-momentum tensor in 3+1 dimensions and derives energy and angular momentum expressions in 2+1 and 1+1 dimensional gravity models.
Findings
Derived symmetric energy-momentum tensor for Einstein-Hilbert action.
Obtained energy and angular momentum expressions in 2+1 dimensions.
Compared gauge theoretical energy in 1+1 dimensions with ADM energy.
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 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.
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