Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations

• Published in: arXiv.org
• Main Authors: Parra-Martinez, Julio, Ruf, Michael S, Zeng, Mao
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 12.01.2021
• Subjects: Approximation; Binary systems; Black holes; Boundary conditions; Differential equations; Field theory; Gravitons; Misalignment; Physics - General Relativity and Quantum Cosmology; Physics - High Energy Physics - Phenomenology; Physics - High Energy Physics - Theory; Scattering angle; Supergravity
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2005.04236

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 Bern et. al. in Einstein gravity and find that they coincide in the high-energy limit, suggesting graviton dominance at this order.