Accelerating Kerr solution in SU(1,1)/U(1)-sigma model

TL;DR

This paper develops a method to generate accelerating Kerr solutions within the SU(1,1)/U(1)-sigma model using inverse scattering, providing a new approach to solving Einstein's equations with acceleration.

Contribution

It introduces a novel application of inverse scattering to derive accelerating Kerr solutions in the sigma model framework, connecting soliton solutions to known spacetime metrics.

Findings

Successfully constructs an accelerating Kerr solution as a three-soliton configuration.

Demonstrates equivalence of the soliton solution to the classical accelerating Kerr metric.

Provides a new technique for generating exact solutions with acceleration in Einstein's theory.

Abstract

Under the coset formulation of pure Einstein spacetime, we solve the reduction problem of the nonlinear \(\sigma\)-model for this spacetime and present the process of the inverse scattering technique after simplification. Through the simplified inverse scattering process, taking the pure Rindler metric as the background, we introduce a pair of solitons on the imaginary axis and obtain an accelerating solution in the form of three solitons in this model. By means of appropriate parameter selection and coordinate transformation, we prove that this accelerating solution in the three-soliton formulation is equivalent to the accelerating Kerr solution.