Quantum Amplitudes Achieve Reconstruction of Spacetime Geometry and Black Hole Signatures

Researchers are increasingly seeking to understand the fundamental connection between quantum mechanics and gravity, and a new study published by Claudio Gambino from Sapienza University of Rome, alongside colleagues, offers a significant step forward. This work presents a novel framework reconstructing classical General Relativity directly from the behaviour of quantum scattering amplitudes, effectively interpreting how spacetime geometry arises from these quantum processes. By linking amplitude analytics to gravitational observables , including metrics and deflection angles , Gambino et al. demonstrate a method for systematically deriving gravitational effects and, crucially, apply this to rotating and charged black holes in various dimensions. The research is particularly noteworthy as it establishes a relativistic link between a source’s internal structure and its external gravitational field, and even provides a pathway to constructing black hole ‘mimickers’ , horizon-less objects sharing similar gravitational signatures, potentially revolutionising our ability to test Einstein’s theory.

Quantum Amplitudes Reconstruct Classical Spacetime Geometry

Scientists have unveiled a groundbreaking framework that reconstructs the entirety of classical General Relativity from the quantum realm of scattering amplitudes. This innovative work interprets the analytic structure within these amplitudes as a direct imprint of spacetime geometry, establishing a precise correspondence between quantum processes and classical gravitational observables like metrics, deflection angles, and multipole moments. Beginning with an effective field theory of gravity, the research demonstrates that loop amplitudes not only incorporate quantum corrections but also encapsulate the nonlinear classical self-interaction of the gravitational field itself. This allows for a systematic derivation of the post-Minkowskian expansion of gravitational quantities, effectively rewriting the Einstein equations in terms of graviton scattering processes, a truly remarkable achievement.
The team achieved a significant breakthrough by extending this framework to rotating and charged sources in arbitrary spacetime dimensions. Utilizing scattering amplitudes of massive spinning fields, they successfully reconstructed the metrics of Kerr, Kerr, Newman, and Myers, Perry black holes, leading to the discovery of higher-dimensional stress multipoles. Furthermore, this approach facilitated an amplitude-based derivation of the universal gyromagnetic factor for charged solutions in higher dimensions, confirming theoretical predictions and opening new avenues for exploration. This work establishes a novel connection between microscopic quantum calculations and macroscopic gravitational phenomena, offering a powerful tool for understanding the universe’s most extreme objects.

Experiments show the development of a momentum-space formulation of the energy-momentum tensor, introducing gravitational form factors and source multipoles that, for the first time, link the internal matter distribution to the external multipolar field in a completely relativistic manner. This innovative approach allows scientists to move beyond traditional approximations and gain a deeper understanding of how matter shapes the gravitational field around it. The research 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 applying it to construct horizon-less compact objects that convincingly mimic the multipolar structure of Kerr black holes. This breakthrough reveals the computation of Fourier transforms of rotating black hole metrics in closed form, exploiting the Kerr-Schild gauge to bridge perturbative and non-perturbative descriptions of gravity. This allows researchers to probe the multipolar structure of higher-dimensional solutions using scattering amplitudes, providing a powerful new method for analyzing these complex systems. The study unveils a pathway to explore the fundamental nature of gravity and black holes, potentially leading to a more complete understanding of the universe and its most enigmatic objects, a truly significant step forward in theoretical physics.

Scattering Amplitudes Reconstruct General Relativity Fully

Scientists have developed a unified framework reconstructing the full classical content of General Relativity from the classical limit of scattering amplitudes. The research establishes a direct correspondence between scattering processes and classical gravitational observables, including metrics, deflection angles, and multipole moments, fundamentally linking microscopic interactions to macroscopic spacetime geometry. Experiments revealed that loop amplitudes not only provide corrections but also encapsulate the nonlinear classical self-interaction of the gravitational field, enabling systematic derivation of the post-Minkowskian expansion of gravitational quantities. This breakthrough rewrites the Einstein equations in terms of graviton scattering processes, offering a novel approach to understanding gravity.

The team measured the exterior spacetime of a rotating axisymmetric body up to second order in angular momentum, reproducing the weak-field limit of the Hartle, Thorne metric in four spacetime dimensions. Extending this work to higher dimensions, the computations successfully recovered the post-Minkowskian expansion of the Myers, Perry family of black hole solutions for specific parameter choices, confirming that information about rotation and multipole structure is entirely contained within the amplitude’s analytic dependence on spin degrees of freedom. Data shows a precise identification of gravitational multipoles in arbitrary dimensions, revealing additional structures beyond those found in four dimensions, termed ‘stress multipoles’, which characterise the spatial part of the metric. Results demonstrate the framework’s ability to distinguish between minimal and non-minimal couplings, with minimal coupling reproducing Kerr geometry, the unique axisymmetric, asymptotically flat vacuum solution, while non-minimal couplings modify the multipole spectrum, capturing more general rotating configurations.

Scientists recorded that spin effects manifest through specific tensorial structures in matter, graviton vertices, with coefficients directly determining the quadrupolar and higher-order multipole moments of the resulting spacetime. Furthermore, the study incorporated electromagnetic interactions, constructing tree- and loop-level amplitudes for massive, electrically charged spinning sources in arbitrary dimensions, revealing how gravitational and electromagnetic exchanges coexist within a diagrammatic expansion. Measurements. Tests prove that introducing a Pauli-type non-minimal coupling restores the expected gyromagnetic behaviour in any dimension, ensuring consistency with the underlying multipolar expansion. This work provides a complete field-theoretic characterization of the gravitational field of spinning bodies and establishes the foundations for advanced multipolar and momentum-space constructions.