论文标题
对称重力闭合
Symmetric gravitational closure
论文作者
论文摘要
我们展示了如何利用对称性假设来确定基于物质场方程的特定几何形状的动态方程。该过程基于物质模型的重力闭合方程，而没有任何对称性的先验假设。足以说明洛伦兹背景上克莱因·戈登场方程的对称过程，通过仔细地施加最大的宇宙学对称性，直接直接在物有的重力封闭方程上，人们就无法获得弗里德曼方程，而没有知道爱因斯坦的方程。这种找到与给定物质动力学兼容的对称性重力场方程的家族直接推广到任何杀死对称的代数，超出标准模型的物质模型，甚至超出了Lorentzian指标以外的紧张时空几何形状。
We show how to exploit symmetry assumptions to determine the dynamical equations for the particular geometry that underpins given matter field equations. The procedure builds on the gravitational closure equations for matter models without any a priori assumption of symmetry. It suffices to illustrate the symmetrization procedure for a Klein-Gordon field equation on a Lorentzian background, for which one obtains the Friedmann equations, without ever having known Einstein's equations, by careful imposition of maximal cosmological symmetry directly on the pertinent gravitational closure equations. This method of finding the family of symmetry-reduced gravitational field equations that are compatible with given matter dynamics directly generalizes to any Killing symmetry algebra, matter models beyond the standard model and indeed tensorial spacetime geometries beyond Lorentzian metrics.
