Wormholes leading to extra dimensions

TL;DR

This paper introduces new static wormhole solutions in 6D general relativity with scalar fields, connecting our universe to a higher-dimensional space with varying sizes of extra dimensions, including explicit examples with different asymptotics.

Contribution

It presents novel 6D wormhole solutions with scalar fields, connecting our universe to a higher-dimensional space with different asymptotic behaviors and explicit metric examples.

Findings

Wormholes connect our universe to a 6D space with small or large extra dimensions.

Explicit solutions with spherical symmetry and toroidal extra dimensions are provided.

Different asymptotic behaviors include constant large extra dimensions and anti-de Sitter infinity.

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 $V(\phi)$ which provides a 6D anti-de Sitter asymptotic, where all spatial dimensions are infinite.