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Mass and Angular Momentum in General Relativity

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Mass and Motion in General Relativity

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 162))

Abstract

We present an introduction to mass and angular momentum in General Relativity. After briefly reviewing energy–momentum for matter fields, first in the flat Minkowski case (Special Relativity) and then in curved spacetimes with or without symmetries, we focus on the discussion of energy–momentum for the gravitational field. We illustrate the difficulties rooted in the Equivalence Principle for defining a local energy–momentum density for the gravitational field. This leads to the understanding of gravitational energy–momentum and angular momentum as nonlocal observables that make sense, at best, for extended domains of spacetime. After introducing Komar quantities associated with spacetime symmetries, it is shown how total energy–momentum can be unambiguously defined for isolated systems, providing fundamental tests for the internal consistency of General Relativity as well as setting the conceptual basis for the understanding of energy loss by gravitational radiation. Finally, several attempts to formulate quasi-local notions of mass and angular momentum associated with extended but finite spacetime domains are presented, together with some illustrations of the relations between total and quasi-local quantities in the particular context of black hole spacetimes. This article is not intended to be a rigorous and exhaustive review of the subject, but rather an invitation to the topic for nonexperts.

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Notes

  1. 1.

    We thank B. Carter for his many comments and insights in this discussion, and in particular for bringing us to the solid state analogy for gravitational masses.

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Acknowledgements

The authors wish to thank the organizers of the Orléans School on Mass for their kind invitation and encouragement.

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Authors and Affiliations

  1. Instituto de Astrofísica de Andalucía, CSIC, 3004, Granada, 18080, Spain

    José Luis Jaramillo

  2. Laboratoire Univers et Théories, Observatoire de Paris, CNRS, Université Paris Diderot, 5 place Jules Janssen, F-92190, Meudon, France

    José Luis Jaramillo & Eric Gourgoulhon

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  1. José Luis Jaramillo
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  2. Eric Gourgoulhon
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Correspondence to José Luis Jaramillo or Eric Gourgoulhon .

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Editors and Affiliations

  1. Institut d'Astrophysique de Paris, boulevard Arago 98bis, Paris, 75014, France

    Luc Blanchet

  2. Observatoire de la Cote d'Azur, Nice, France

    Alessandro Spallicci

  3. Dept. Physics, University of Florida, Gainesville, 32611-8440, Florida, USA

    Bernard Whiting

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Jaramillo, J.L., Gourgoulhon, E. (2009). Mass and Angular Momentum in General Relativity. In: Blanchet, L., Spallicci, A., Whiting, B. (eds) Mass and Motion in General Relativity. Fundamental Theories of Physics, vol 162. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3015-3_4

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