Ellipsoidal, Cylindrical, Bipolar and Toroidal Wormholes in 5D Gravity

TL;DR

This paper introduces new anisotropic 5D wormhole and flux tube solutions with various geometries, demonstrating their properties and the use of anholonomic frames to handle local anisotropy in vacuum Einstein equations.

Contribution

It constructs novel anisotropic 5D wormhole solutions with diverse geometries using anholonomic frames, extending previous isotropic models.

Findings

Solutions exhibit gravitational charge scaling due to anisotropy.

Various 3D hypersurface geometries are realizable within these solutions.

In isotropic limit, solutions reduce to known 5D wormholes.

Abstract

In this paper we construct and analyze new classes of wormhole and flux tube-like 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 [vst]. 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.