We describe the construction of traversable wormholes with multiple mouths in four spacetime dimensions and discuss associated quantum entanglement. Our wormholes may be traversed between any pair of mouths. In particular, in the three-mouth case they have fundamental group F2 (the free group on two generators). By contrast, connecting three regions A, B, C in pairs (AB, BC, and AC) using three separate wormholes would give fundamental group F3. Our solutions are asymptotically flat up to the presence of possible magnetic fluxes or cosmic strings that extend to infinity. The construction begins with a two-mouth traversable wormhole supported by backreaction from quantum fields. Inserting a sufficiently small black hole into its throat preserves traversability between the original two mouths. This black hole is taken to be the mouth of another wormhole connecting the original throat to a new distant region of spacetime. Making the new wormhole traversable in a manner similar to the original two-mouth wormhole provides the desired causal connections. From a dual field theory point of view, when AdS asymptotics are added to our construction, multiparty entanglement may play an important role in the traversability of the resulting wormhole.
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].
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].
P. Gao, D. L. Jafferis and A. C. Wall, Traversable Wormholes via a Double Trace Deformation, JHEP 12 (2017) 151 [arXiv:1608.05687] [INSPIRE].
J. Maldacena and X.-L. Qi, Eternal traversable wormhole, arXiv:1804.00491 [INSPIRE].
J. Maldacena, A. Milekhin and F. Popov, Traversable wormholes in four dimensions, arXiv:1807.04726 [INSPIRE].
Z. Fu, B. Grado-White and D. Marolf, A perturbative perspective on self-supporting wormholes, Class. Quant. Grav. 36 (2019) 045006 [Erratum ibid. 36 (2019) 249501] [arXiv:1807.07917] [INSPIRE].
E. Caceres, A. S. Misobuchi and M.-L. Xiao, Rotating traversable wormholes in AdS, JHEP 12 (2018) 005 [arXiv:1807.07239] [INSPIRE].
D. Marolf and S. McBride, Simple Perturbatively Traversable Wormholes from Bulk Fermions, JHEP 11 (2019) 037 [arXiv:1908.03998] [INSPIRE].
Z. Fu, B. Grado-White and D. Marolf, Traversable Asymptotically Flat Wormholes with Short Transit Times, Class. Quant. Grav. 36 (2019) 245018 [arXiv:1908.03273] [INSPIRE].
G. T. Horowitz, D. Marolf, J. E. Santos and D. Wang, Creating a Traversable Wormhole, Class. Quant. Grav. 36 (2019) 205011 [arXiv:1904.02187] [INSPIRE].
J. Maldacena and A. Milekhin, SYK wormhole formation in real time, JHEP 04 (2021) 258 [arXiv:1912.03276] [INSPIRE].
M. Headrick, V. E. Hubeny, A. Lawrence and M. Rangamani, Causality & holographic entanglement entropy, JHEP 12 (2014) 162 [arXiv:1408.6300] [INSPIRE].
M. A. Melvin, Pure magnetic and electric geons, Phys. Lett. 8 (1964) 65 [INSPIRE].
R. Emparan, Black diholes, Phys. Rev. D 61 (2000) 104009 [hep-th/9906160] [INSPIRE].
R. Emparan and E. Teo, Macroscopic and microscopic description of black diholes, Nucl. Phys. B 610 (2001) 190 [hep-th/0104206] [INSPIRE].
A. C. Wall, The Generalized Second Law implies a Quantum Singularity Theorem, Class. Quant. Grav. 30 (2013) 165003 [Erratum ibid. 30 (2013) 199501] [arXiv:1010.5513] [INSPIRE].
S. Gao and R. M. Wald, Theorems on gravitational time delay and related issues, Class. Quant. Grav. 17 (2000) 4999 [gr-qc/0007021] [INSPIRE].
R. Bousso, Z. Fisher, S. Leichenauer and A. C. Wall, Quantum focusing conjecture, Phys. Rev. D 93 (2016) 064044 [arXiv:1506.02669] [INSPIRE].
M. Visser, Lorentzian wormholes: From Einstein to Hawking, Amer. Inst. of Physics (1995) [INSPIRE].
J. Maldacena and A. Milekhin, Humanly traversable wormholes, Phys. Rev. D 103 (2021) 066007 [arXiv:2008.06618] [INSPIRE].
R. Emparan and M. Gutperle, From p-branes to fluxbranes and back, JHEP 12 (2001) 023 [hep-th/0111177] [INSPIRE].
A. Al Balushi, Z. Wang and D. Marolf, Traversability of Multi-Boundary Wormholes, JHEP 04 (2021) 083 [arXiv:2012.04635] [INSPIRE].
D. Marolf, H. Maxfield, A. Peach and S. F. Ross, Hot multiboundary wormholes from bipartite entanglement, Class. Quant. Grav. 32 (2015) 215006 [arXiv:1506.04128] [INSPIRE].
C. Akers and P. Rath, Entanglement Wedge Cross Sections Require Tripartite Entanglement, JHEP 04 (2020) 208 [arXiv:1911.07852] [INSPIRE].
K. Umemoto and T. Takayanagi, Entanglement of purification through holographic duality, Nature Phys. 14 (2018) 573.
V. Balasubramanian, P. Hayden, A. Maloney, D. Marolf and S. F. Ross, Multiboundary Wormholes and Holographic Entanglement, Class. Quant. Grav. 31 (2014) 185015 [arXiv:1406.2663] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Diving into traversable wormholes, Fortsch. Phys. 65 (2017) 1700034 [arXiv:1704.05333] [INSPIRE].
B. Freivogel, D. A. Galante, D. Nikolakopoulou and A. Rotundo, Traversable wormholes in AdS and bounds on information transfer, JHEP 01 (2020) 050 [arXiv:1907.13140] [INSPIRE].
D. Berenstein, Quenches on thermofield double states and time reversal symmetry, Phys. Rev. D 100 (2019) 066022 [arXiv:1906.08292] [INSPIRE].
V. Cardoso, E. Franzin, A. Maselli, P. Pani and G. Raposo, Testing strong-field gravity with tidal Love numbers, Phys. Rev. D 95 (2017) 084014 [Addendum ibid. 95 (2017) 089901] [arXiv:1701.01116] [INSPIRE].
F. J. Ernst, Removal of the nodal singularity of the C-metric, J. Math. Phys. 17 (1976) 515.
D. Garfinkle and A. Strominger, Semiclassical Wheeler wormhole production, Phys. Lett. B 256 (1991) 146 [INSPIRE].
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Emparan, R., Grado-White, B., Marolf, D. et al. Multi-mouth traversable wormholes. J. High Energ. Phys. 2021, 32 (2021). https://doi.org/10.1007/JHEP05(2021)032
- AdS-CFT Correspondence
- Black Holes