Generating Gowdy cosmological models

TL;DR

This paper introduces a method to generate new analytic Gowdy cosmological models from initial data, expanding the set of known solutions to Einstein's equations for these models.

Contribution

The authors develop a novel technique to construct Gowdy cosmological solutions from initial singularity data, including explicit examples like Kantowski-Sachs models.

Findings

Generated new Gowdy solutions from initial data.

Provided formal general solution for arbitrary initial conditions.

Constructed explicit examples such as Kantowski-Sachs models.

Abstract

Using the analogy with stationary axisymmetric solutions, we present a method to generate new analytic cosmological solutions of Einstein's equation belonging to the class of $T^3$ Gowdy cosmological models. We show that the solutions can be generated from their data at the initial singularity and present the formal general solution for arbitrary initial data. We exemplify the method by constructing the Kantowski-Sachs cosmological model and a generalization of it that corresponds to an unpolarized $T^3$ Gowdy model.