论文标题
对所有订单的一般相对论的扰动和一般$ n^{\ rm th} $订单条款
Perturbations of General Relativity to All Orders and the General $n^{\rm th}$ Order Terms
论文作者
论文摘要
我们为Einstein-Hilbert Action和Einstein方程的扰动提供了全阶表达式，并具有一般的$ n $ th订单条款。为此，我们在张量密度和通常的度量张量形式主义（包括爱因斯坦 - 迪拉顿理论）中采用了Cheung和Remmen的扰动惯例。值得注意的是，我们发现最小的构建块为我们的每种配方产生了整个扰动。我们表明，随着扰动的顺序增加，扰动的术语数量增长。我们将结果视为参考，并讨论如何从参考中获得其他约定的扰动。作为一致性检查，我们使用基于扰动爱因斯坦方程的扰动方法计算重力散射幅度。最后，我们讨论了如何将结果推广到弯曲的背景并结合其他问题。
We derive all-order expressions for perturbations of the Einstein-Hilbert action and the Einstein equation with the general $n$-th order terms. To this end, we employ Cheung and Remmen's perturbation conventions both in tensor density and the usual metric tensor formalisms, including the Einstein-dilaton theory. Remarkably, we find minimal building blocks that generate the entire perturbations for each of our formulations. We show that the number of terms of perturbations grows linearly as the order of perturbations increases. We regard our results as the reference and discuss how to derive perturbations in other conventions from the reference. As a consistency check, we compute graviton scattering amplitudes using the perturbiner method based on the perturbative Einstein equation. Finally we discuss how to generalise the results to curved backgrounds and incorporate additional matter.
