Ellipsoidal, cylindrical, bipolar and toroidal wormholes in 5D gravity

In this article we construct and analyze new classes of wormhole and flux tubelike solutions for the 5D vacuum Einstein equations. These 5D solutions possess generic local anisotropy which gives rise to a gravitational running or scaling of the Kaluza-Klein electric and magnetic charges of these solutions. It is also shown that it is possible to self-consistently construct these anisotropic solutions with various rotational 3D hypersurface geometries (i.e., ellipsoidal, cylindrical, bipolar and toroidal). The local anisotropy of these solutions is handled using the technique of anholonomic frames with their associated nonlinear connection structures [S. Vacaru, Ann. Phys. (N.Y.) 256, 39 (1997); Nucl. Phys. B 434, 590 (1997); J. Math. Phys. 37, 508 (1996); J. High Energy Phys. 09: 011 (1998); Phys. Lett. B 498, 74 (2001)]. Through the use of the anholonomic frames the metrics are diagonalized, in contrast to holonomic coordinate frames where the metrics would have off-diagonal components. In the local isotropic limit these solutions are shown to be equivalent to spherically symmetric 5D wormhole and flux tube solutions. (C) 2002 American Institute of Physics.