Locally anisotropic wormholes and flux tubes in 5D gravity

In this Letter we examine a class of wormhole and flux tube like solutions to 5D vacuum Einstein equations. These solutions possess generic local anisotropy, and their local isotropic limit is shown to be conformally equivalent to the spherically symmetric 5D solutions by Dzhunushaliev and Singleton [Phys. Rev. D 59 (1999) 064018]. The anisotropic solutions investigated here have two physically distinct signatures: first, they can give rise to angular-dependent, anisotropic “electromagnetic” interactions. Second, they can result in a gravitational running of the “electric” and “magnetic” charges of the solutions. This gravitational running of the electromagnetic charges is linear rather than logarithmic, and could thus serve as an indirect signal for the presence of higher dimensions. The local anisotropy of these solutions is modeled using the technique of anholonomic frames with respect to which the metrics are diagonalized. If holonomic coordinate frames were used then such metrics would have off-diagonal components.