论文标题
散射幅度和N体后，孟沃斯基的汉密尔顿人一般相对论及以后
Scattering Amplitudes and N-Body Post-Minkowskian Hamiltonians in General Relativity and Beyond
论文作者
论文摘要
我们提出了一个通用框架，用于计算孟斯科斯基后，古典，保守的哈密顿人，以$ n $ n $ spinning尸体的相对论散射幅度的一般相对论。描述了$ n> 2 $的新型功能，包括按下树状迭代贡献的减法以及计算构建位置空间电位所需的非平凡多体傅立叶变换积分。根据区域方法描述了一种将这些积分作为分层限制扩展的新方法。作为一个明确的例子，我们介绍了$ \ Mathcal {o} \ left（g^2 \ right）$ 3体动量空间潜力以及Einstein-Maxwell的带电物体。结果证明，在一般相对论中，最高$ \ MATHCAL {O} \ left（g^2 v^4 \ right）$中的牛顿后的计算完全一致。此外，在适当的限制中，结果证明与多中心极端黑洞背景中的相对论探针散射以及模质空间近似中缓慢移动的极端黑洞的散射。
We present a general framework for calculating post-Minskowskian, classical, conservative Hamiltonians for $N$ non-spinning bodies in general relativity from relativistic scattering amplitudes. Novel features for $N>2$ are described including the subtraction of tree-like iteration contributions and the calculation of non-trivial many-body Fourier transform integrals needed to construct position space potentials. A new approach to calculating these integrals as an expansion in the hierarchical limit is described based on the method of regions. As an explicit example, we present the $\mathcal{O}\left(G^2\right)$ 3-body momentum space potential in general relativity as well as for charged bodies in Einstein-Maxwell. The result is shown to be in perfect agreement with previous post-Newtonian calculations in general relativity up to $\mathcal{O}\left(G^2 v^4\right)$. Furthermore, in appropriate limits the result is shown to agree perfectly with relativistic probe scattering in multi-center extremal black hole backgrounds and with the scattering of slowly-moving extremal black holes in the moduli space approximation.
