Generating new gravitational solutions by matrix multiplication

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-03-06 DOI:10.1098/rspa.2023.0857
M. Cristina Câmara, Gabriel Lopes Cardoso
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Abstract

Explicit solutions to the nonlinear field equations of some gravitational theories can be obtained, by means of a Riemann–Hilbert approach, from a canonical Wiener–Hopf factorization of certain matrix functions called monodromy matrices. In this paper, we describe other types of factorization 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 factorization 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 factorization, provided the latter exists, and that one can superpose such solutions. Examples of applications include Kasner, Einstein–Rosen wave and gravitational pulse wave solutions.

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通过矩阵乘法生成新的引力解
某些引力理论的非线性场方程的显式解可以通过黎曼-希尔伯特(Riemann-Hilbert)方法,从称为单色矩阵(monodromy matrices)的某些矩阵函数的典型维纳-霍普夫(Wiener-Hopf)因式分解中获得。在本文中,我们将介绍其他类型的因式分解,从中可以用类似的方法构建解。我们的方法基于一个不变量问题,它并不构成黎曼-希尔伯特(Riemann-Hilbert)问题,而且可以构建单色矩阵的 Wiener-Hopf 因式分解无法获得的解。它催生了一种基于矩阵乘法的新型解生成方法。我们特别指出,只要存在典型的维纳-霍普夫因式分解,就可以通过乘法变形得到新的解,而且可以叠加这些解。应用实例包括卡斯纳波、爱因斯坦-罗森波和引力脉冲波的求解。
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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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