论文标题
通过矩阵乘法生成新的重力解决方案
Generating new gravitational solutions by matrix multiplication
论文作者
论文摘要
通过Riemann-Hilbert方法，可以从某些称为单片矩阵的某些矩阵函数的典范Wiener-HopF分解中，可以通过Riemann-Hilbert方法获得某些引力理论的非线性场方程的明确解。在本文中，我们描述了可以以类似方式构建解决方案的其他类型的分解。我们的方法是基于不变性问题，该问题不构成Riemann-Hilbert问题，并允许构建通过Wiener-Hopf分解单型基质而无法获得的解决方案。它引起了基于矩阵乘法的新颖解决方案生成方法。我们特别表明，只要存在后者，就可以通过对规范的维也纳-HOPF分解的乘法变形来获得新的解决方案，并且可以超级置于此类溶液。应用的示例包括Kasner，Einstein-Rosen波和重力脉冲波解决方案。
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.
