2020/10/31 by Stavros Mougiakakos, Pierre Vanhove · 1 citation
Physics and Astronomy · #hep-th #gr-qc
paper · pdf · doi:10.1103/physrevd.103.026001
published as Phys. Rev. D 103, 026001 (2021) · latex. 44 pages. v2 : several minor corrections. Version to appear in Phys. Rev. D
arxiv created 2020/12/20 · arxiv updated 2021/01/13
We derive the static Schwarzschild-Tangherlini metric by extracting the classical contributions from the multi-loop vertex functions of a graviton emitted from a massive scalar field. At each loop orders the classical contribution is proportional to a unique master integral given by the massless sunset integral. By computing the scattering amplitudes up to three-loop order in general dimension, we explicitly derive the expansion of the metric up to the fourth post-Minkowskian order O(GN4) in four, five and six dimensions. There are ultraviolet divergences that are cancelled with the introduction of higher-derivative non-minimal couplings. The standard Schwarzschild-Tangherlini is recovered by absorbing their effects by an appropriate coordinate transformation induced from the de Donder gauge condition.