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arXiv · 2403.13216

The Schwarzschild Black Hole from Perturbation Theory to all Orders

Poul H. Damgaard·Kanghoon Lee
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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.

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Poul H. Damgaard, Kanghoon Lee. 2024-03-20. The Schwarzschild Black Hole from Perturbation Theory to all Orders. https://arxiv.org/abs/2403.13216

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