Generating new gravitational solutions by matrix multiplication
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866911971585032192 |
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| author | Câmara, M. Cristina Cardoso, Gabriel Lopes |
| author_facet | Câmara, M. Cristina Cardoso, Gabriel Lopes |
| contents | Explicit solutions to the non-linear field equations of some gravitational theories can be obtained, by means of a Riemann-Hilbert approach, from a canonical Wiener-Hopf factorisation of certain matrix functions called monodromy matrices. In this paper we describe other types of factorisation from which solutions can be constructed in a similar way. Our approach is based on an invariance problem, which does not constitute a Riemann-Hilbert problem and allows to construct solutions that could not have been obtained by Wiener-Hopf factorisation of a monodromy matrix. It gives rise to a novel solution generating method based on matrix multiplications. We show, in particular, that new solutions can be obtained by multiplicative deformation of the canonical Wiener-Hopf factorisation, provided the latter exists, and that one can superpose such solutions. Examples of applications include Kasner, Einstein-Rosen wave and gravitational pulse wave solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_01702 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Generating new gravitational solutions by matrix multiplication Câmara, M. Cristina Cardoso, Gabriel Lopes Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Analysis of PDEs Functional Analysis Explicit solutions to the non-linear field equations of some gravitational theories can be obtained, by means of a Riemann-Hilbert approach, from a canonical Wiener-Hopf factorisation of certain matrix functions called monodromy matrices. In this paper we describe other types of factorisation from which solutions can be constructed in a similar way. Our approach is based on an invariance problem, which does not constitute a Riemann-Hilbert problem and allows to construct solutions that could not have been obtained by Wiener-Hopf factorisation of a monodromy matrix. It gives rise to a novel solution generating method based on matrix multiplications. We show, in particular, that new solutions can be obtained by multiplicative deformation of the canonical Wiener-Hopf factorisation, provided the latter exists, and that one can superpose such solutions. Examples of applications include Kasner, Einstein-Rosen wave and gravitational pulse wave solutions. |
| title | Generating new gravitational solutions by matrix multiplication |
| topic | Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2211.01702 |