Journal of High Energy Physics

, 2019:37 | Cite as

Simple perturbatively traversable wormholes from bulk fermions

  • Donald Marolf
  • Sean McBrideEmail author
Open Access
Regular Article - Theoretical Physics


A new class of traversable wormholes was recently constructed which relies only on local bulk dynamics rather than an explicit coupling between distinct boundaries. Here we begin with a four-dimensional Weyl fermion field of any mass m propagating on a classical background defined by a Z2 quotient of (rotating) BTZ × S1. This setup allows one to compute the fermion stress-energy tensor exactly. For appropriate boundary conditions around a non-contractible curve, perturbative back-reaction at any m renders the associated wormhole traversable and suggests it can become eternally traversable at the limit where the background becomes extremal. A key technical step is the proper formulation of the method of images for fermions in curved spacetime. We find the stress- energy of spinor fields to have important kinematic differences from that of scalar fields, typically causing the sign of the integrated null stress-energy (and thus in many cases the sign of the time delay/advance) to vary around the throat of the wormhole. Similar effects may arise for higher-spin fields.


Black Holes Gauge-gravity correspondence 


Open Access

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  1. [1]
    A. Einstein and N. Rosen, The particle problem in the general theory of relativity, Phys. Rev.48 (1935) 73 [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    R.W. Fuller and J.A. Wheeler, Causality and multiply connected space-time, Phys. Rev.128 (1962) 919 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    H.G. Ellis, Ether flow through a drainhole: a particle model in general relativity, J. Math. Phys.14 (1973) 104.ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    M.S. Morris and K. S. Thorne, Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity, Amer. J. Phys.56 (1988) 395.ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    M.S. Morris, K.S. Thorne and U. Yurtsever, Wormholes, time machines and the weak energy condition, Phys. Rev. Lett.61 (1988) 1446 [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    O. James, E. von Tunzelmann, P. Franklin and K.S. Thorne, Visualizing Interstellar’s Wormhole, Am. J. Phys.83 (2015) 486 [arXiv:1502.03809] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    J.L. Friedman, K. Schleich and D.M. Witt, Topological censorship, Phys. Rev. Lett.71 (1993) 1486 [Erratum ibid.75 (1995) 1872] [gr-qc/9305017] [INSPIRE].
  8. [8]
    G.J. Galloway, K. Schleich, D.M. Witt and E. Woolgar, Topological censorship and higher genus black holes, Phys. Rev.D 60 (1999) 104039 [gr-qc/9902061] [INSPIRE].
  9. [9]
    E. Ayon-Beato, F. Canfora and J. Zanelli, Analytic self-gravitating Skyrmions, cosmological bounces and AdS wormholes, Phys. Lett.B 752 (2016) 201 [arXiv:1509.02659] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    F. Canfora, N. Dimakis and A. Paliathanasis, Topologically nontrivial configurations in the 4d Einstein-nonlinear σ-model system, Phys. Rev.D 96 (2017) 025021 [arXiv:1707.02270] [INSPIRE].
  11. [11]
    N. Graham and K.D. Olum, Achronal averaged null energy condition, Phys. Rev.D 76 (2007) 064001 [arXiv:0705.3193] [INSPIRE].
  12. [12]
    A.C. Wall, Proving the achronal averaged null energy condition from the generalized second law, Phys. Rev.D 81 (2010) 024038 [arXiv:0910.5751] [INSPIRE].
  13. [13]
    J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  14. [14]
    P. Gao, D.L. Jafferis and A.C. Wall, Traversable wormholes via a double trace deformation, JHEP12 (2017) 151 [arXiv:1608.05687] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    J. Maldacena, D. Stanford and Z. Yang, Diving into traversable wormholes, Fortsch. Phys.65 (2017) 1700034 [arXiv:1704.05333] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    T.G. Mertens, G.J. Turiaci and H.L. Verlinde, Solving the Schwarzian via the conformal bootstrap, JHEP08 (2017) 136 [arXiv:1705.08408] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  17. [17]
    J. Maldacena and X.-L. Qi, Eternal traversable wormhole, arXiv:1804.00491 [INSPIRE].
  18. [18]
    E. Caceres, A.S. Misobuchi and M.-L. Xiao, Rotating traversable wormholes in AdS, JHEP12 (2018) 005 [arXiv:1807.07239] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys.61 (2013) 781 [arXiv:1306.0533] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    L. Susskind and Y. Zhao, Teleportation through the wormhole, Phys. Rev.D 98 (2018) 046016 [arXiv:1707.04354] [INSPIRE].
  21. [21]
    L. Susskind, Dear qubitzers, GR=QM, arXiv:1708.03040 [INSPIRE].
  22. [22]
    J. Maldacena, A. Milekhin and F. Popov, Traversable wormholes in four dimensions, arXiv:1807.04726 [INSPIRE].
  23. [23]
    Z. Fu, B. Grado-White and D. Marolf, A perturbative perspective on self-supporting wormholes, Class. Quant. Grav.36 (2019) 045006 [arXiv:1807.07917] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    Z. Fu, B. Grado-White and D. Marolf, Traversable asymptotically flat wormholes with short transit times, arXiv:1908.03273 [INSPIRE].
  25. [25]
    M. Bañados, C. Teitelboim and J. Zanelli, The black hole in three-dimensional space-time, Phys. Rev. Lett.69 (1992) 1849 [hep-th/9204099] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2+1) black hole, Phys. Rev.D 48 (1993) 1506 [Erratum ibid.D 88 (2013) 069902] [gr-qc/9302012] [INSPIRE].
  27. [27]
    J. Louko and D. Marolf, Single exterior black holes and the AdS/CFT conjecture, Phys. Rev.D 59 (1999) 066002 [hep-th/9808081] [INSPIRE].
  28. [28]
    I. Ichinose and Y. Satoh, Entropies of scalar fields on three-dimensional black holes, Nucl. Phys.B 447 (1995) 340 [hep-th/9412144] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept.323 (2000) 183 [hep-th/9905111] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    J. Polchinski, String theory. Volume 2: superstring theory and beyond, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (2007).Google Scholar
  31. [31]
    M. de Jesus Anguiano Galicia and A. Bashir, Fermions in odd space-time dimensions: Back to basics, Few Body Syst.37 (2005) 71 [hep-ph/0502089] [INSPIRE].
  32. [32]
    D. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge U.K. (2012).CrossRefGoogle Scholar
  33. [33]
    P. Di Francesco, P. Mathieu, and D. Senechal, Conformal field theory, Graduate Texts in Contemporary Physics, Springer, Germany (1997).Google Scholar
  34. [34]
    W. Mueck, Spinor parallel propagator and Green’s function in maximally symmetric spaces, J. Phys.A 33 (2000) 3021 [hep-th/9912059] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  35. [35]
    B. Allen and T. Jacobson, Vector two point functions in maximally symmetric spaces, Commun. Math. Phys.103 (1986) 669 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  36. [36]
    S. Hirano, Y. Lei and S. van Leuven, Information transfer and black hole evaporation via traversable BTZ wormholes, JHEP09 (2019) 070 [arXiv:1906.10715] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    B. Freivogel, D.A. Galante, D. Nikolakopoulou and A. Rotundo, Traversable wormholes in AdS and bounds on information transfer, arXiv:1907.13140 [INSPIRE].
  38. [38]
    H. Nastase, Introduction to the ADS/CFT correspondence, Cambridge University Press, Cambridge U.K. (2015).CrossRefGoogle Scholar
  39. [39]
    V.E. Ambruş, Dirac fermions on rotating space-times, Ph.D. thesis, University of Sheffield, Sheffield, U.K. (2014).Google Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.

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