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Relativity in Modern Physics$
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Nathalie Deruelle and Jean-Philippe Uzan

Print publication date: 2018

Print ISBN-13: 9780198786399

Published to Oxford Scholarship Online: October 2018

DOI: 10.1093/oso/9780198786399.001.0001

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Conservation laws

Conservation laws

(p.443) 5 Conservation laws
Relativity in Modern Physics

Nathalie Deruelle

Jean-Philippe Uzan

Oxford University Press

This chapter studies how the ‘spacetime symmetries’ can generate first integrals of the equations of motion which simplify their solution and also make it possible to define conserved quantities, or ‘charges’, characterizing the system. As already mentioned in the introduction to matter energy–momentum tensors in Chapter 3, the concepts of energy, momentum, and angular momentum are related to the invariance properties of the solutions of the equations of motion under spacetime translations or rotations. The chapter explores these in greater detail. It first turns to isometries and Killing vectors. The chapter then examines the first integrals of the geodesic equation, and Noether charges.

Keywords:   conservation laws, spacetime symmetries, first integrals, invariance properties, isometries, Killing vectors, geodesic equation, Noether charges

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