New insights into black hole scattering and gravitational waves unveiled

The cover of Nature Volume 641, Issue 8063 features the study by Dr Gustav Mogull and colleagues. Their research provides a high-precision prediction of black hole scattering. Credit: Mathias Driesse/Humboldt University Berlin.

This research, led by Professor Jan Plefka at Humboldt University of Berlin and Queen Mary University London’s Dr Gustav Mogull, formerly at Humboldt Universität and the Max Planck Institute for Gravitational Physics (Albert Einstein Institute), and conducted in collaboration with an international team of physicists, provides unprecedented precision in calculations crucial to understanding gravitational waves. 

Using cutting-edge techniques inspired by quantum field theory, the team calculated the fifth post-Minkowskian (5PM) order for observables such as scattering angles, radiated energy, and recoil. A groundbreaking aspect of the work is the appearance of Calabi-Yau three-fold periods – geometric structures rooted in string theory and algebraic geometry – within the radiative energy and recoil. These structures, once considered purely mathematical, now find relevance in describing real-world astrophysical phenomena. 

With gravitational wave observatories like LIGO entering a new phase of sensitivity and next-generation detectors such as LISA on the horizon, this research meets the increasing demand for theoretical models of extraordinary accuracy. 

Dr Mogull explained the significance:

While the physical process of two black holes interacting and scattering via gravity we’re studying is conceptually simple the level of mathematical and computational precision required is immense.

Benjamin Sauer, PhD candidate at Humboldt University of Berlin adds: “The appearance of Calabi-Yau geometries deepens our understanding of the interplay between mathematics and physics. These insights will shape the future of gravitational wave astronomy by improving the templates we use to interpret observational data." 

This precision is particularly important for capturing signals from elliptic bound systems, where orbits more closely resemble high-velocity scattering events, a domain where traditional assumptions about slow-moving black holes no longer apply. 

Gravitational waves, ripples in spacetime caused by accelerating massive objects, have revolutionised astrophysics since their first detection in 2015. The ability to model these waves with precision enhances our understanding of cosmic phenomena, including the “kick” or recoil of black holes after scattering – a process with far-reaching implications for galaxy formation and evolution. 

Perhaps most tantalisingly, the discovery of Calabi-Yau structures in this context connects the macroscopic realm of astrophysics with the intricate mathematics of quantum mechanics. “This could fundamentally change how physicists approach these functions,” said team member Dr Uhre Jakobsen of Max Planck Institute for Gravitational Physics and Humboldt University of Berlin. “By demonstrating their physical relevance, we can focus on specific examples that illuminate genuine processes in nature.” 

The project utilised over 300,000 core hours of high-performance computing at the Zuse Institute Berlin to solve the equations governing black hole interactions, demonstrating the indispensable role of computational physics in modern science. “The swift availability of these computing resources was key to the success of the project,” adds PhD candidate Mathias Driesse, who led the computing efforts. 

Professor Plefka emphasised the collaborative nature of the work: “This breakthrough highlights how interdisciplinary efforts can overcome challenges once deemed insurmountable. From mathematical theory to practical computation, this research exemplifies the synergy needed to push the boundaries of human knowledge.” 

This breakthrough not only advances the field of gravitational wave physics but also bridges the gap between abstract mathematics and the observable universe, paving the way for discoveries yet to come. The collaboration is set to expand its efforts further, exploring higher-order calculations and utilising the new results in future gravitational waveform models. Beyond theoretical physics, the computational tools used in this study, such as KIRA, also have applications in fields like collider physics. 

This achievement was the result of extensive international collaboration and advanced mathematical and computational methods. The groundwork for the study was laid in Plefka’s group at Humboldt University of Berlin, where the Worldline Quantum Field Theory formalism was pioneered together with Dr Gustav Mogull. Over time, the collaboration expanded to include world-leading specialists such as Dr Johann Usovitsch, who moved from CERN to Humboldt University of Berlin and is the developer of the KIRA software, as well as mathematical physicists Dr Christoph Nega (Technical University of Munich) and Professor Albrecht Klemm (University of Bonn), leading experts on Calabi-Yau manifolds. 

The project received key funding through Professor Plefka’s ERC Advanced Grant GraWFTy, the RTG 2575 Rethinking Quantum Field Theory, and the novel Research Unit FOR 5582 of the Deutsche Forschungsgemeinschaft, in which Plefka and Klemm are principal investigators. It was also supported by Dr Mogull’s Royal Society University Research Fellowship, Gravitational Waves from Worldline Quantum Field Theory.