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Wormholes, Warp Drives and Energy Conditions pp 111–135Cite as

Self-Sustained Traversable Wormholes

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

Abstract

In this contribution, we consider self-sustained traversable wormholes, which are configurations sustained by their own gravitational quantum fluctuations. The investigation is evaluated through a variational approach with Gaussian trial wave functionals to one loop, and the graviton quantum fluctuations are interpreted as a kind of exotic energy. Since these fluctuations usually produce ultraviolet (UV) divergences, we introduce two procedures to keep them under control. The first consists of a zeta function regularization and a renormalization process that is introduced to obtain a finite one loop energy. The second approach considers the case of distorted gravity, namely, when either Gravity’s Rainbow or a noncommutative geometry is used as a tool to keep under control the UV divergences. It is shown that for every framework, the self-sustained equation will produce a Wheeler wormhole of Planckian size. Some consequences on topology change are discussed together with the possibility of obtaining an enlarged wormhole radius.

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Notes

  1. 1.

    See for example Refs. [6, 7] to see how the Casimir procedure comes into play for ZPE calculations.

  2. 2.

    See also Refs. [10,11,12,13], where the authors search for classical traversable wormholes supported by phantom energy.

  3. 3.

    To this purpose, see also paper of Hochberg, Popov, and Sushkov [14], and the paper of Khusnutdinov and Sushkov [15].

  4. 4.

    Note that our approach is very close to the gravitational geon considered by Anderson and Brill [18]. The relevant difference is in the averaging procedure.

  5. 5.

    Details on sign conventions and decomposition of the Einstein tensor can be found in Sect. 6.2.1.

  6. 6.

    See also Refs. [22, 23] for further details on the decomposition of the perturbation at the quantum level.

  7. 7.

    Note that sometimes the effective masses are related to the three-dimensional Lichnerowicz operator defined in [24], whose form is

    figure a
  8. 8.

    It is interesting to note that the inhomogeneous case, namely \(p_{r}=\omega \left( r\right) \rho ^{\gamma }\) potentially can produce results [31].

  9. 9.

    Of course, one could also consider a generalized uncertainty principle (GUP) to obtain finite results. However, it is easy to see that if one postulates the validity of Gravity’s Rainbow, to obtain modified dispersion relations one necessarily has to impose

    figure b

    namely plane wave solutions which remain plane, even if the metric is described by Eq. (6.100); only in this way can one argue that the modified dispersion relations are a consequence of gravity’s rainbow. However, if we relax the condition of imposing plane wave solutions even at the Planck scale, the distorted metric, Eq. (6.100), leads to a GUP which differs from the Heisenberg uncertainty principle, by terms linear and quadratic in particle momenta. The GUP-induced terms become relevant near the Planck scale and lead to the existence of a minimum measurable length. This could be interpreted as the breakdown of the validity of continuum space–time at very small scales.

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Authors and Affiliations

  1. Dipartimento di Ingegneria e scienze applicate, Università degli Studi di Bergamo, Viale Marconi, 5, 24044, Dalmine (Bergamo), Italy

    Remo Garattini

  2. I.N.F.N. - sezione di Milano, Milan, Italy

    Remo Garattini

  3. Faculdade de Ciências, Instituto de Astrofísica e Ciências do Espaço, Universidade de Lisboa, Campo Grande, 1749-016, Lisboa, Portugal

    Francisco S. N. Lobo

Authors
  1. Remo Garattini
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  2. Francisco S. N. Lobo
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Correspondence to Remo Garattini .

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

    Francisco S. N. Lobo

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Garattini, R., Lobo, F.S.N. (2017). Self-Sustained Traversable Wormholes. 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_6

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