Heterotic Footprints in Classical Gravity: PM dynamics from On-Shell soft amplitudes at one loop
Arpan Bhattacharyya, Saptaswa Ghosh, Ankit Mishra, Sounak Pal
TL;DR
The paper tackles the classical two-body dynamics of charged black holes in Einstein–Maxwell–Dilaton theory at one-loop order in the Post-Minkowskian expansion, seeking string-inspired imprints on classical gravity. It employs scattering-amplitude methods, soft-loop expansions, and eikonal exponentiation, together with Lippmann–Schwinger–based potential extraction and IR subtraction, to produce IR-finite, conservative observables. Key contributions include a detailed separation of electromagnetic and dilatonic charge effects in the potential and scattering angle, robust GR-limit checks, and building-block results suitable for waveform modeling in beyond-GR theories. The work provides amplitude-based benchmarks for compact-object dynamics in EMD and outlines a path toward higher PM orders, inclusion of spin and finite-size effects, and incorporation of radiation-reaction in waveform predictions.
Abstract
We study classical scattering of charged black holes in Einstein-Maxwell-Dilaton (EMD) theory. Working in the classical (Post-Minkowskian) regime, we extract the conservative two-body potential by expanding the one loop amplitudes in the soft regime. We show explicitly that, as in GR, the relevant soft amplitudes are infrared (IR) finite once the long-range interactions are consistently treated via Lippmann-Schwinger equation and the associated IR subtraction. The scattering angle is then obtained from the eikonal exponentiation of the soft amplitude. Our results track the separate roles of electromagnetic and dilatonic charges in both the conservative dynamics and the eikonal phase, and they reduce smoothly to the GR limit when the charges and dilaton coupling are switched off. Where applicable, we compare with existing results in the literature and find agreement. These findings provide amplitude-based benchmarks for compact-object dynamics in EMD and furnish building blocks for waveform modeling in beyond-GR scenarios.