From Quantum Amplitudes to Spacetime Geometry: a Multipolar Framework for Black Hole Signatures

TL;DR

This thesis develops a comprehensive framework linking quantum scattering amplitudes to classical spacetime geometry, enabling the systematic derivation of gravitational observables and the construction of black hole mimickers with detailed multipolar structures.

Contribution

It introduces a novel multipolar framework connecting quantum amplitudes with classical gravitational fields, including black hole mimickers and higher-dimensional solutions.

Findings

Derived post-Minkowskian expansion from amplitudes

Linked internal matter distribution to external multipoles

Computed black hole metrics in closed form using Fourier transforms

Abstract

This thesis develops a unified framework that reconstructs the full classical content of General Relativity from the classical limit of quantum scattering amplitudes. By interpreting the analytic structure of amplitudes as the field-theoretic imprint of spacetime geometry, the work establishes a direct correspondence between quantum processes and classical gravitational observables such as metrics, deflection angles, and multipole moments. Starting from the effective-field-theory description of gravity, the thesis shows that loop amplitudes encode not only quantum corrections but also the nonlinear classical self-interaction of the gravitational field, enabling the systematic derivation of the post-Minkowskian expansion of gravitational quantities by rewriting the Einstein equations in terms of graviton scattering processes. Building upon this foundation, the framework is applied to rotating and charged sources in arbitrary spacetime dimensions. A momentum-space formulation of the energy-momentum tensor is then developed, introducing gravitational form factors and source multipoles that link, for the first time, the internal matter distribution to the external multipolar field in a completely relativistic framework. Furthermore, the thesis completes the transition from the microscopic amplitude picture to the macroscopic description of gravitational sources by engineering a multipole-based framework for black hole mimickers, then applied to build horizon-less compact objects mimicking the multipolar structure of Kerr black holes. Finally, exploiting the Kerr-Schild gauge, the Fourier transforms of rotating black hole metrics are computed in closed form, bridging perturbative and non-perturbative descriptions of gravity, and allowing to probe the multipolar structure of higher-dimensional solutions employing scattering amplitudes.