Factorisation of symmetric matrices and applications in gravitational theories
| Title: | Factorisation of symmetric matrices and applications in gravitational theories |
|---|---|
| Authors: | Câmara, M. Cristina, Cardoso, Gabriel Lopes |
| Publication Year: | 2024 |
| Collection: | Mathematics General Relativity and Quantum Cosmology Mathematical Physics |
| Subject Terms: | Mathematics - Functional Analysis, General Relativity and Quantum Cosmology, Mathematical Physics |
| More Details: | We consider the canonical Wiener-Hopf factorisation of $2 \times 2$ symmetric matrices $\mathcal M$ with respect to a contour $\Gamma$. 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. Comment: 20 pages |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2410.16514 |
| Accession Number: | edsarx.2410.16514 |
| Database: | arXiv |
| Description not available. |