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Gravity and the Quantum pp 89–98Cite as

Piecewise Conserved Quantities

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Part of the book series: Fundamental Theories of Physics ((FTPH,volume 187))

Abstract

We review the treatment of conservation laws in spacetimes that are glued together in various ways, thus adding a boundary term to the usual conservation laws. Several examples of such spacetimes will be described, including the joining of Schwarzschild spacetimes of different masses, and the possibility of joining regions of different signatures. The opportunity will also be taken to explore some of the less obvious properties of Lorentzian vector calculus.

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Notes

  1. 1.

    We assume the metrics \(g^\pm _{ab}\) are non-degenerate on \(\varSigma \), the only other possibility.

  2. 2.

    My recent textbook on general relativity [23] also uses this language.

References

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Acknowledgements

It is a pleasure to thank the many collaborators who contributed to my work on piecewise smooth manifolds, including especially Chris Clarke, George Ellis, Charles Hellaby, Gerard ’t Hooft, Corinne Manogue, and Robin Tucker.

Author information

Authors and Affiliations

  1. Department of Mathematics, Oregon State University, Corvallis, OR, 97331, USA

    Tevian Dray

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  1. Tevian Dray
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Correspondence to Tevian Dray .

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Editors and Affiliations

  1. Department of Physical Sciences, IISER Mohali, Mohali, Punjab, India

    Jasjeet Singh Bagla

  2. Ryussi Technologies Pvt. Ltd., Pune, India

    Sunu Engineer

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Dray, T. (2017). Piecewise Conserved Quantities. In: Bagla, J., Engineer, S. (eds) Gravity and the Quantum. Fundamental Theories of Physics, vol 187. Springer, Cham. https://doi.org/10.1007/978-3-319-51700-1_8

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