We apply a formulation of Einstein’s general relativity with only cubic interactions for deriving the metric of a Schwarzschild black hole to all orders in perturbation theory. This cubic interactions formulation coupled to effective worldline action of a massive point particle allows to derive a recursion relation for the form factors of the off-shell graviton emission current. The unique solution to the recursion relation leads to the Schwarzschild black-hole solution in four dimensions. This provides the first derivation of the black hole metric from a matter source to all orders in perturbation theory from an amplitude approach. Published by the American Physical Society 2024

中文翻译：

---

从散射振幅到 GN 中所有阶次的 Schwarzschild 度量


我们应用爱因斯坦广义相对论的公式，仅用三次相互作用来推导出史瓦西黑洞的度量到微扰理论中的所有阶次。这种三次相互作用公式与大质量点粒子的有效世界线作用相结合，可以推导出离壳引力子发射电流的形状因子的递归关系。递归关系的唯一解导致了四维的 Schwarzschild 黑洞解。这提供了从物质源到振幅方法的微扰理论中所有阶次的黑洞度量的首次推导。 美国物理学会 2024 年出版