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Breakthrough in Gravitational Wave Physics: Scattering of Black Holes Described with Unprecedented Precision

Study provides new insights into the gravitational interactions between colliding black holes and answers to fundamental questions in physics

Under the leadership of Prof Dr Jan Plefka from the Department of Physics at Humboldt-Universität zu Berlin (HU), an international team has described the dynamics of colliding black holes with unprecedented mathematical precision. Their study, published in the renowned journal Physical Review Letters, provides new insights into the gravitational interactions between these objects in our universe.

Black holes are the objects with the highest mass density in our universe. Their gravitational force is so enormous that even light cannot escape. When the black holes move towards each other, gravitational waves are emitted - a phenomenon that Albert Einstein described back in 1915 in his General Theory of Relativity and which has already been observed at gravitational wave detectors such as the Laser Interferometer Gravitational-Wave Observatory, LIGO, in the USA.

A combination of methods enables a precise description

The team of physicists from Humboldt-Universität, the Max Planck Institute for Gravitational Physics in Potsdam and CERN near Geneva, Switzerland, has now calculated the scattering of two black holes and the interactions resulting from the gravitational pull between the two masses with high precision. To do this, they have applied methods from quantum field theory and particle physics to the classical two-body problem in physics. This approach, which required state-of-the-art mathematical integration techniques and high-performance computers, enabled them to achieve a whole new level of precision.

"Resolving this problem marks a new frontier for multi-loop calculations and effective field theory techniques," says Jan Plefka, head of the Quantum Field and String Theory Group at the Department of Physics at Humboldt-Universität. "We had to optimise every aspect, from the integrand generation to developing new integration-by-parts methods," adds Benjamin Sauer, co-author and PhD student in the research group. In total, around five hundred thousand 16-dimensional integrals describing the scattering angle had to be reduced to 470 basic master integrals, which were then calculated.

High precision gravitational wave models for a future detector in space

With their calculations, the physicists have provided an approximate solution to the fundamental two-body problem and at the same time laid the foundation for advanced gravitational wave models that will be needed for next-generation detectors - such as the Laser Interferometer Space Antenna, LISA, a gravitational wave detector that the European Space Agency plans to build in space. The higher precision will enable exquisitely accurate tests of Einstein's theory and new insights into the nuclear and gravitational physics of binary systems of rotating black holes.

"Our results bring the prediction of gravitational waves from encounters between two black holes to an unprecedented level of accuracy," says Gustav Uhre Jakobsen, co-author and researcher in Plefka’s group. "This opens up brilliant new avenues for extracting statements on fundamental questions of physics from future gravitational wave observations."

Further Information

Research article: Conservative Black Hole Scattering at Fifth Post-Minkowskian and First Self-Force Order


Prof. Dr. Jan Plefka
Department of Physics at Humboldt-Universität zu Berlin