Factorisation of symmetric matrices and applications in gravitational theories
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915987812515840 |
|---|---|
| author | Câmara, M. Cristina Cardoso, Gabriel Lopes |
| author_facet | Câmara, M. Cristina Cardoso, Gabriel Lopes |
| contents | We consider the canonical Wiener-Hopf factorisation of $2 \times 2$ symmetric matrices $\mathcal M$ with respect to a contour $Γ$. For the case that the quotient $q$ of the two diagonal elements of $\mathcal M$ is a rational function, we show that due to the symmetric nature of the matrix $\mathcal M$, the second column in each of the two matrix factors that arise in the factorisation is determined in terms of the first column in each of these matrix factors, by multiplication by a rational matrix, and we give a method for determining the second columns of these factors. We illustrate our method with two examples in the context of a Riemann-Hilbert approach to obtaining solutions to the Einstein field equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16514 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Factorisation of symmetric matrices and applications in gravitational theories Câmara, M. Cristina Cardoso, Gabriel Lopes Functional Analysis General Relativity and Quantum Cosmology Mathematical Physics We consider the canonical Wiener-Hopf factorisation of $2 \times 2$ symmetric matrices $\mathcal M$ with respect to a contour $Γ$. For the case that the quotient $q$ of the two diagonal elements of $\mathcal M$ is a rational function, we show that due to the symmetric nature of the matrix $\mathcal M$, the second column in each of the two matrix factors that arise in the factorisation is determined in terms of the first column in each of these matrix factors, by multiplication by a rational matrix, and we give a method for determining the second columns of these factors. We illustrate our method with two examples in the context of a Riemann-Hilbert approach to obtaining solutions to the Einstein field equations. |
| title | Factorisation of symmetric matrices and applications in gravitational theories |
| topic | Functional Analysis General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2410.16514 |