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9 - Noether’s Theorems and Energy in General Relativity

Published online by Cambridge University Press:  22 September 2022

James Read
Affiliation:
Pembroke College, Oxford
Nicholas J. Teh
Affiliation:
University of Notre Dame, Indiana
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Summary

This chapter has three main aims. First, it gives a pedagogical introduction to Noether’s two theorems and their implications for energy conservation in general relativity, which was a central point of discussion between Hilbert, Klein, Noether, and Einstein. Second, it introduces and compares two proposals for gravitational energy and momentum, one of which is very influential in physics, and neither of which has been discussed in the philosophical literature. Third, it assesses these proposals in connection with recent philosophical discussions of energy and momentum in general relativity. After briefly reviewing the debates about energy conservation between Hilbert, Klein, Noether, and Einstein, the chapter shows that Einstein’s gravitational energy-momentum pseudo-tensor, including its superpotential, is fixed, through Noether’s theorem, by the boundary terms in the action. That is, the freedom to add an arbitrary superpotential to the gravitational pseudo-tensor corresponds to the freedom to add boundary terms to the action without changing the equations of motion. This freedom is fixed in the same way for both problems. The chapter also includes a review of two proposals for energy and momentum in GR: one is a quasi-local alternative to the local expressions, and the other builds on Einstein’s local pseudo-tensor approach.

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Chapter
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The Philosophy and Physics of Noether's Theorems
A Centenary Volume
, pp. 197 - 256
Publisher: Cambridge University Press
Print publication year: 2022

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