Scattering amplitudes and \(N\)-body post-Minkowskian Hamiltonians in general relativity and beyond

DOI10.1007/JHEP02(2023)105arXiv2208.02281MaRDI QIDQ6045647

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Publication date: 12 May 2023

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Abstract: 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 $mathcalOleft(G^{2}ight)$ 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 $mathcalOleft(G^2{v}^{4}ight)$. 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.

Full work available at URL: https://arxiv.org/abs/2208.02281

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