Warped, anisotropic wormhole/soliton configurations in vacuum 5D gravity

Abstract

In this paper we apply the anholonomic frames method developed in previous work to construct and study anisotropic vacuum field configurations in 5D gravity. Starting with an off-diagonal 5D metric, parametrized 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 choose 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 has an exponential warp factor similar to that of the Randall–Sundrum model. However, the warp factor depends on more than just the fifth coordinate. In addition the warp factor arises from anisotropic vacuum solutions 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.