The Schwarzschild Black Hole from Perturbation Theory to all Orders
Abstract
Applying the quantum field theoretic perturbiner approach to Einstein gravity, we compute the metric of a Schwarzschild black hole order by order in perturbation theory. Using recursion, this calculation can be carried out in de Donder gauge to all orders in Newton's constant. The result is a geometric series which is convergent outside a disk of finite radius, and it agrees within its region of convergence with the known de Donder gauge metric of a Schwarzschild black hole. It thus provides a first all-order perturbative computation in Einstein gravity with a matter source, and this series converges to the known non-perturbative expression in the expected range of convergence.
Keywords
Cite
@article{arxiv.2403.13216,
title = {The Schwarzschild Black Hole from Perturbation Theory to all Orders},
author = {Poul H. Damgaard and Kanghoon Lee},
journal= {arXiv preprint arXiv:2403.13216},
year = {2024}
}
Comments
7 pages, no figure; v2: references added; v3: one reference added, version to appear in Physical Review Letters