广义相对论中的格林函数
Green's function in general relativity
AI总结：
本研究提出弯曲时空动量空间新定义及不依赖弱场近似的 Einstein 方程自由场线性化方法，并给出平面波与 Schwarzschild 引力场格林函数。
摘要：
本报告给出了广义相对论中出现的引力场的格林函数（经典传播子）。借助 Hodge 调和分析，确保了在具有不定度规的弯曲空间中波动方程格林函数的存在性。格林函数的解析性由内在方式决定，以保持因果性。本报告提出了弯曲时空中动量空间的一种新定义，以及将 Einstein 方程线性化为与 Yang-Mills 规范场相一致的自由场。所提出的线性化并不使用弱场近似；因此，该方法适用于高度弯曲的时空。我们给出了两个引力场格林函数的例子：平面波解和 Schwarzschild 解。
英文摘要：
This report provides Green's functions (classical propagators) of gravitational fields appearing in general relativity. The existence of Green's function of the wave equation in curved space with an indefinite metric is ensured owing to the Hodge harmonic analysis. The analyticity of Green's function is determined intrinsically to keep a causality. This report proposed a novel definition of momentum space in curved space-time and the linearisation of the Einstein equation as a free field consistent with that of the Yang-Mills gauge field. The proposed linearisation does not utilize the weak-field approximation; thus, the method applies to highly caved space-time. We gave two examples of Green's function of gravitational fields: the plane wave solution and the Schwarzschild solution.
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