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The Schwarzschild Black Hole from Perturbation Theory to all Orders

High Energy Physics - Theory 2024-05-31 v3 General Relativity and Quantum Cosmology

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