Warped, Anisotropic Wormhole/Soliton Configurations in Vacuum 5D Gravity

TL;DR

This paper constructs anisotropic vacuum solutions in 5D gravity using anholonomic frames, revealing new warp factors and solitonic structures that could model particles or gravitational waves without matter.

Contribution

It introduces a method to generate anisotropic 5D vacuum solutions with solitonic features using anholonomic frames, expanding the understanding of higher-dimensional gravity configurations.

Findings

Existence of anisotropic vacuum solutions with warp factors depending on multiple coordinates.

Solutions include solitons of KP and sine-Gordon equations embedded in 5D gravity.

Potential interpretations as particle models or nonlinear gravitational waves.

Abstract

In this paper we apply the anholonomic frames method developed in refs. [1-4] to construct and study anisotropic vacuum field configurations in 5D gravity. Starting with an off--diagonal 5D metric, parameterized in terms of several ansatz functions, we show that using anholonomic frames greatly simplifies the resulting Einstein field equations. These simplified equations contain an interesting freedom in that one can chose one of the ansatz functions and then determine the remaining ansatz functions in terms of this choice. As examples we take one of the ansatz functions to be a solitonic solution of either the Kadomtsev-Petviashvili equation or the sine-Gordon equation. There are several interesting physical consequences of these solutions. First, a certain subclass of the solutions discussed in this paper have an exponential warp factor similar to that of the Randall-Sundrum model. However, the warp factor depends on more than just the 5$^{th}$ coordinate. In addition the warp factor arises from anisotropic vacuum solution rather than from any explicit matter. Second, the solitonic character of these solutions might allow them to be interpreted either as gravitational models for particles (i.e. analogous to the ' t Hooft-Polyakov monopole, but in the context of gravity), or as nonlinear, anisotropic gravitational waves.