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Extremal black hole scattering at \(\mathcal{O} (G^3)\): graviton dominance, eikonal exponentiation, and differential equations. (English) Zbl 1456.83117
Summary: We use \(\mathcal{N} = 8\) supergravity as a toy model for understanding the dynamics of black hole binary systems via the scattering amplitudes approach. We compute the conservative part of the classical scattering angle of two extremal (half-BPS) black holes with minimal charge misalignment at \(\mathcal{O} (G^3)\) using the eikonal approximation and effective field theory, finding agreement between both methods. We construct the massive loop integrands by Kaluza-Klein reduction of the known \(D\)-dimensional massless integrands. To carry out integration we formulate a novel method for calculating the post-Minkowskian expansion with exact velocity dependence, by solving velocity differential equations for the Feynman integrals subject to modified boundary conditions that isolate conservative contributions from the potential region. Motivated by a recent result for universality in massless scattering, we compare the scattering angle to the result found by Z. Bern et al. [J. High Energy Phys. 2019, No. 10, Paper No. 206, 135 p. (2019; Zbl 1427.83035)] in Einstein gravity and find that they coincide in the high-energy limit, suggesting graviton dominance at this order.

MSC:
83E50 Supergravity
83E15 Kaluza-Klein and other higher-dimensional theories
83C57 Black holes
83C10 Equations of motion in general relativity and gravitational theory
81U05 \(2\)-body potential quantum scattering theory
Software:
Fuchsia; epsilon
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