Smooth Gowdy-symmetric generalised Taub-NUT solutions with polynomial initial data
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916437440856064 |
|---|---|
| author | Hennig, Jörg |
| author_facet | Hennig, Jörg |
| contents | We consider smooth Gowdy-symmetric generalised Taub-NUT solutions, a class of inhomogeneous cosmological models with spatial three-sphere topology. They are characterised by existence of a smooth past Cauchy horizon and, with the exception of certain singular cases, they also develop a regular future Cauchy horizon. Several examples of exact solutions were previously constructed, where the initial data (in form of the initial Ernst potentials) are polynomials of low degree. Here, we generalise to polynomial initial data of arbitrary degree. Utilising methods from soliton theory, we obtain a simple algorithm that allows us to construct the resulting Ernst potential with purely algebraic calculations. We also derive an explicit formula in terms of determinants, and we illustrate the method with two examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10028 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Smooth Gowdy-symmetric generalised Taub-NUT solutions with polynomial initial data Hennig, Jörg General Relativity and Quantum Cosmology Mathematical Physics We consider smooth Gowdy-symmetric generalised Taub-NUT solutions, a class of inhomogeneous cosmological models with spatial three-sphere topology. They are characterised by existence of a smooth past Cauchy horizon and, with the exception of certain singular cases, they also develop a regular future Cauchy horizon. Several examples of exact solutions were previously constructed, where the initial data (in form of the initial Ernst potentials) are polynomials of low degree. Here, we generalise to polynomial initial data of arbitrary degree. Utilising methods from soliton theory, we obtain a simple algorithm that allows us to construct the resulting Ernst potential with purely algebraic calculations. We also derive an explicit formula in terms of determinants, and we illustrate the method with two examples. |
| title | Smooth Gowdy-symmetric generalised Taub-NUT solutions with polynomial initial data |
| topic | General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2410.10028 |