Warped Solitonic Deformations and Propagation of Black Holes in 5D Vacuum Gravity

TL;DR

This paper constructs exact 5D vacuum gravity solutions with off-diagonal metrics, revealing anisotropic warp factors and solitonic propagating black holes, linking soliton configurations to noncommutative field theories.

Contribution

It introduces a method to generate exact 5D vacuum solutions with off-diagonal metrics, including black holes that propagate solitonically, connecting solitons and noncommutative theories.

Findings

Black hole solutions propagate as solitons in 5D spacetime.

Solutions exhibit anisotropic warp factors and physical parameter scaling.

Connections established between solitonic solutions and noncommutative field theory.

Abstract

In this paper we use the anholonomic frames method to construct exact solutions for vacuum 5D gravity with metrics having off-diagonal components. The solutions are in general anisotropic and possess interesting features such as an anisotropic warp factor with respect to the extra dimension, or a gravitational scaling/running of some of the physical parameters associated with the solutions. A certain class of solutions are found to describe Schwarzschild black holes which ``solitonically'' propagate in spacetime. The solitonic character of these black hole solutions arises from the embedding of a 3D soliton configuration (e.g. the soliton solutions to the Kadomtsev-Petviashvily or sine-Gordon equations) into certain ansatz functions of the 5D metric. These solitonic solutions may either violate or preserve local Lorentz invariance. In addition there is a connection between these solutions and noncommutative field theory.