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Classical and Semi-classical Energy Conditions

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Wormholes, Warp Drives and Energy Conditions

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 189))

Abstract

The standard energy conditions of classical general relativity are (mostly) linear in the stress–energy tensor, and have clear physical interpretations in terms of geodesic focussing, but suffer the significant drawback that they are often violated by semi-classical quantum effects. In contrast, it is possible to develop non-standard energy conditions that are intrinsically nonlinear in the stress–energy tensor, and which exhibit much better well-controlled behaviour when semi-classical quantum effects are introduced, at the cost of a less direct applicability to geodesic focussing. In this chapter, we will first review the standard energy conditions and their various limitations. (Including the connection to the Hawking–Ellis type I, II, III, and IV classification of stress–energy tensors). We shall then turn to the averaged, nonlinear, and semi-classical energy conditions, and see how much can be done once semi-classical quantum effects are included.

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Notes

  1. 1.

    There have been interesting attempts to derive the NCC from an underlying fundamental framework [4,5,6,7].

  2. 2.

    For type II Hawking and Ellis choose to set \(f\rightarrow \pm 1\), which we find unhelpful.

  3. 3.

    For type III Hawking and Ellis choose to set \(f\rightarrow 1\), which we find unhelpful.

  4. 4.

    For type IV Hawking and Ellis choose

    figure a

    We have found the version presented in the text to be more useful.

  5. 5.

    Note that stable violations of the NEC are now known to be possible when the field has a non-canonical kinetic term [18,19,20].

  6. 6.

    See Refs. [26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48] for interesting research along those lines.

  7. 7.

    Interesting studies include (but are not limited to) Refs. [78,79,80,81,82,83,84].

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Acknowledgements

PMM acknowledges financial support from the Spanish Ministry of Economy and Competitiveness through the postdoctoral training contract FPDI-2013-16161, and through the project FIS2014-52837-P. MV acknowledges financial support via the Marsden Fund administered by the Royal Society of New Zealand.

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Authors and Affiliations

  1. Departamento de Física Teórica I, Ciudad Universitaria, Universidad Complutense de Madrid, 28040, Madrid, Spain

    Prado Martín–Moruno

  2. School of Mathematics and Statistics, Victoria University of Wellington, PO Box 600, Wellington, 6140, New Zealand

    Matt Visser

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  1. Prado Martín–Moruno
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Correspondence to Matt Visser .

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  1. Departamento de Física da FCUL , Lisboa, Grande Lisboa, Portugal

    Francisco S. N. Lobo

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Martín–Moruno, P., Visser, M. (2017). Classical and Semi-classical Energy Conditions. In: Lobo, F. (eds) Wormholes, Warp Drives and Energy Conditions. Fundamental Theories of Physics, vol 189. Springer, Cham. https://doi.org/10.1007/978-3-319-55182-1_9

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