One of the most profound problems in general relativity

From October 20-22, 2025, international experts will gather at the Max Planck Institute for Gravitational Physics in Potsdam to explore the history and development of the relativistic two-body problem.

Just over 50 years ago, the discovery of the Hulse–Taylor binary pulsar proved the existence of gravitational waves. Since then, significant progress has been made culminating in the first detection of a gravitational wave emitted by a binary black hole merger in 2015 by the LIGO and Virgo Collaboration. This progress has emerged from a complex interplay of analytical, numerical, and experimental advances. The workshop, “In Pursuit of Gravitational Waves: Solving the Two-Body Problem in General Relativity” will bring together leading physicists, historians, and philosophers to examine the historical, conceptual, and methodological developments that have shaped the evolution of one of the most profound challenges of general relativity: the relativistic two-body problem.

“We aim to investigate how analytical and numerical relativity methods have developed and interacted over time, and how they contributed to the discovery of gravitational waves in 2015,” says Alessandra Buonanno, director of the Astrophysical and Cosmological Relativity department at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute, AEI) in the Potsdam Science Park. “The workshop will be an opportunity to reflect on the methods, conceptual challenges, and broader contexts that have shaped this remarkable scientific journey.”

Jean-Philippe Martinez, a Balzan Fellow in the history and philosophy of physics at the AEI and one of the workshop organizers, adds: “We hope to shed light on how different research traditions, institutional settings, and collaborative dynamics have guided the development of the field and continue to influence its directions today.”

The relativistic two-body problem

In the two-body problem of general relativity, the objective is to determine the dynamical evolution of two massive objects—such as black holes or neutron stars—mutually influencing each other through gravity while emitting gravitational waves. These waves carry imprints of the system’s properties, enabling researchers to infer critical astrophysical parameters, including masses, spins, and tidal deformabilities, especially during the late inspiral, merger, and ringdown phases. General relativity describes gravity as the curvature of spacetime, governed by highly nonlinear Einstein field equations. Due to this nonlinearity, exact analytical solutions are generally unattainable, and only approximate or special-case solutions exist. To overcome this limitation, numerical-relativity simulations—performed on high-performance supercomputers—provide highly accurate solutions by solving the full Einstein equations in a dynamical setting. However, these simulations are computationally intensive and resource demanding. As a result, a synergistic approach combining analytical with numerical relativity has become indispensable. Together, these methods enable the construction of precise waveform models, which are essential for detecting gravitational-wave signals and extracting their astrophysical, cosmological, and fundamental physics implications.

The success of gravitational-wave astronomy

On September 14, 2015, the Laser Interferometer Gravitational-Wave Observatory (LIGO) made the first direct detection of gravitational waves—GW150914—from the merger of two black holes, marking a historic milestone in physics and astronomy. Since then, continuous advancements in detector sensitivity, sophisticated waveform modeling, and powerful data analysis techniques have dramatically enhanced our ability to observe the universe through gravitational waves. As of now, over 300 confirmed binary coalescences—primarily of black holes—have been detected across multiple observing runs, providing an unprecedented census of compact binary systems and revealing new insights into stellar evolution and strong-field gravity.

The Balzan Prize project

The workshop, hosted by the “Astrophysical and Cosmological Relativity” department at the AEI in Potsdam, is part of the Balzan Prize project. The project examines the historical and philosophical aspects of solving the two-body problem in general relativity. It focuses on the development of analytical and numerical approaches, as well as the interplay – and contrasts – between these methods. The project is funded by the 2021 Balzan Prize, which Buonanno received in the field of “Gravitation: Physical and Astrophysical Aspects”.

Topics of the workshop

The event will feature twelve historical, philosophical, and forward-looking talks, along with three panel discussions centered on the following key themes:

• Why did progress in analytical relativity differ in Europe compared to the US, and more generally among countries?
• Why did progress in numerical relativity differ in Europe compared to the US, and more generally among countries?
• Appreciation, competition, and synergism between analytical and numerical relativity approaches.

Contributions from experimentalists and data analysts will also be included to highlight how theoretical modeling informs and responds to observational work.