Abstract
In 6D general relativity with a scalar field as a source of gravity, a new type of static wormhole solutions is presented: such wormholes connect our universe with a small 2D extra subspace with a universe where this extra subspace is large, and the whole space-time is effectively 6-dimensional. We consider manifolds with the structure M0 × M1 × M2, where M0 is 2D Lorentzian space-time while each of M1,2 can be a 2-sphere or a 2-torus. After selecting possible asymptotic behaviors of the metric functions compatible with the field equations, we give two explicit examples of wormhole solutions with spherical symmetry in our space-time and toroidal extra dimensions. In one example, with a massless scalar field (it is a special case of a well-known more general solution), the extra dimensions have a large constant size at the “far end”; the other example contains a nonzero potential V(φ) which provides a 6D anti-de Sitter asymptotic, where all spatial dimensions are infinite.
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References
K. A. Bronnikov and S. G. Rubin, Black Holes, Cosmology, and Extra Dimensions (World Scientific, 2012).
V. N. Melnikov, Grav. Cosmol. 22, 80–96 (2016).
V. D. Ivashchuk and V. N. Melnikov, Grav. Cosmol. 22, 166–178 (2016).
T. Clifton, P. G. Ferreira, A. Padilla, and C. Skordis, “Modified gravity and cosmology,” Phys. Rep. 513, 1–189 (2012); arXiv: 1106.2476.
S. G. Rubin, “Interpenetrating subspaces as a funnel to extra space,” Phys. Lett. B 759, 622 (2016); arXiv: 1603.03880.
M. Visser, LorentzianWormholes: fromEinstein to Hawking (AIP, Woodbury, 1995).
F. S. N. Lobo, “Exotic solutions in general relativity: traversable wormholes and warp drive" spacetimes,” in Classical and Quantum Gravity Research (Nova Sci. Pub., 2008), p. 1–78; arXiv: 0710.4474.
V. Dzhunushaliev, V. Folomeev, and A. Urazalina, Int. J. Mod. Phys. D 24, 1550097 (2015); arXiv: 1506.03897.
K. A. Bronnikov and A. M. Galiakhmetov, Grav. Cosmol. 21, 283 (2015); arXiv: 1508.01114.
R. Myrzakulov, L. Sebastiani, S. Vagnozzi, and S. Zerbini, Class. Quantum Grav. 33 (12), 125005 (2016); arXiv: 1510.02284.
R. Aurich, S. Lustig, F. Steiner, and H. Then, Class. Quantum Grav. 21, 4901 (2004); astro-ph/0403597.
Frank Steiner, “Do black holes exist in a finite universe having the topology of a flat 3-torus?,” arXiv: 1608.03133.
D. Hochberg and M. Visser, Phys. Rev. D 56, 4745 (1997); gr-qc/9704082.
K. A. Bronnikov and A. A. Starobinsky, Pis’ma v ZhETF 85, 3–8 (2007); JETP Lett. 85 1–5 (2007); gr-qc/0612032.
K. A. Bronnikov, M. V. Skvortsova, and A. A. Starobinsky, Grav. Cosmol. 16, 216–222 (2010); ArXiv: 1005.3262.
K. A. Bronnikov and Sung-Won Kim, Phys. Rev. D 67, 064027 (2003); gr-qc/0212112.
G. Dotti, J. Oliva, and R. Troncoso, Phys. Rev. D 76, 064038 (2007); arXiv: 0706.1830.
T. Harko, F. S. N. Lobo, M. K. Mak, and S. V. Sushkov, Phys. Rev. D87, 067504 (2013); arXiv: 1301.6878.
K. A. Bronnikov, J. C. Fabris, and S. V. B. Gonçalves, J. Phys. A:Math. Theor. 40, 6835–6840 (2007).
K. A. Bronnikov, Grav. Cosmol. 1, 67 (1995); grqc/ 9505020.
K. A. Bronnikov, V. D. Ivashchuk, and V. N. Melnikov, Grav. Cosmol. 3, 205 (1997); gr-qc/9710054.
K. A. Bronnikov, Acta Phys. Pol. B 4, 251 (1973).
H. G. Ellis, J. Math. Phys. 14, 104 (1973).
K. A. Bronnikov and J. C. Fabris, Phys. Rev. Lett. 96, 251101 (2006); gr-qc/0511109.
K. A. Bronnikov, V. N. Melnikov, and H. Dehnen, Gen. Rel. Grav. 39, 973 (2007); gr-qc/0611022.
S. V. Bolokhov, K. A. Bronnikov, and M. V. Skvortsova, Class. Quantum Grav. 29, 245006 (2012); arXiv: 1208.4619.
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Bronnikov, K.A., Skvortsova, M.V. Wormholes leading to extra dimensions. Gravit. Cosmol. 22, 316–322 (2016). https://doi.org/10.1134/S0202289316040058
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DOI: https://doi.org/10.1134/S0202289316040058