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Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon, and M. Zeng, Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order, Phys. Rev. Lett. 122
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Similar

A. Cristofoli, P. H. Damgaard, P. Di Vecchia, and C. Heissenberg, Second-order Post-Minkowskian scattering in arbitrary dimensions, JHEP 07
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2003
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A. Petrov and J. B. Pitts, The Field-Theoretic Approach in General Relativity and Other Metric Theories. A Review, (2020), arXiv:2004.10525 [gr-qc]
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2004
Cited alongside, same era.
N. E. J. Bjerrum-Bohr, J. F. Donoghue, and B. R. Holstein, Quantum corrections to the Schwarzschild and Kerr metrics, Phys. Rev. D 68
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N. Bjerrum-Bohr, J. F. Donoghue, and B. R. Holstein, Quantum gravitational corrections to the nonrelativistic scattering potential of two masses, Phys. Rev. D 67

Then

R. Emparan and H. S. Reall, Black Holes in Higher Dimensions, Living Rev. Rel. 11
Original
2008
Later among the works it cites.
Z. Bern, J. J. M. Carrasco, and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory, Phys. Rev. Lett. 105
Original
2010
Later among the works it cites.
C. Cheung and G. N. Remmen, Twofold Symmetries of the Pure Gravity Action, JHEP 01
Original
2017
Later among the works it cites.
N. J. Bjerrum-Bohr, P. H. Damgaard, G. Festuccia, L. Planté, and P. Vanhove, General Relativity from Scattering Amplitudes, Phys. Rev. Lett. 121
Original
2018
Later among the works it cites.
C. Cheung, I. Z. Rothstein, and M. P. Solon, From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion, Phys. Rev. Lett. 121

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2020

Schwarzschild-Tangherlini Metric from Scattering Amplitudes

Jakobsen, Gustav Uhre

Understand

We present a general framework with which the Schwarzschild-Tangherlini metric of a point particle in arbitrary dimensions can be derived from a scattering amplitude to all orders in the gravitational constant, $G_N$, in covariant gauge (i.e.

$R_\xi$-gauge) with a generalized de Donder-type gauge function, $G_\sigma$.
The metric is independent of the covariant gauge parameter $\xi$ and obeys the classical gauge condition $G_\sigma=0$.
We compute the metric with the generalized gauge choice explicitly to second order in $G_N$ where gravitational self-interactions become important and these results verify the general framework to one-loop order.