Wormholes leading to extra dimensions
arXiv:1608.04974 · doi:10.1134/S0202289316040058
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 x M1 x M2 , where M0 is 2D Lorentzian space-time while each of M1 an M2 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 which provides a 6D anti-de Sitter asymptotic, where all spatial dimensions are infinite.
8 pages, 1 figure of 2 parts. Minor corrections
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- The Schwarzschild singularity: a semiclassical bounce?
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