تقرير
Generating new gravitational solutions by matrix multiplication
| العنوان: | Generating new gravitational solutions by matrix multiplication |
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| المؤلفون: | Câmara, M. Cristina, Cardoso, Gabriel Lopes |
| المصدر: | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (2024) |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics, General Relativity and Quantum Cosmology, High Energy Physics - Theory, Mathematics - Analysis of PDEs, Mathematics - Functional Analysis |
| الوصف: | 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. Comment: 29 pages; v2:various improvements |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1098/rspa.2023.0857 |
| الوصول الحر: | http://arxiv.org/abs/2211.01702Test |
| رقم الانضمام: | edsarx.2211.01702 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1098/rspa.2023.0857 |
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