To the point:
- New detectors: Over the next decade, new gravitational-wave observatories on Earth and in space will begin operations. They will be much more sensitive than current detectors and will observe signals in much greater detail.
- New models: The waveform models used for data analysis — mathematical methods for calculating the expected signals — must be about 100 times more accurate than the current models in order to exploit the full potential of the new observatories.
- Important milestone: Researchers at the Max Planck Institute for Gravitational Physics in Potsdam, together with international colleagues, have now taken the most difficult step towards new, more precise analytical waveform models. They have improved methods from particle physics, enabling predictions to be made with unprecedented precision across the four fundamental forces.
Breakthrough on the path to highly accurate prediction of gravitational-wave signals
The key to understanding black holes
Pairs of merging black holes reveal their presence only through their gravitational waves and remain invisible to other astronomical methods. The first gravitational wave, detected 11 years ago by the LIGO detectors, originated from such a merger. Even today, the vast majority of the nearly 400 published signals originate from merging black holes. Gravitational-wave astronomy has evolved into a successful method of observing and studying the dark side of the universe.
To detect and understand these signals, scientists need not only highly sensitive laser interferometers but also precisely tailored waveform models. These mathematical predictions provide the templates that researchers use to identify the signals in the observational data.
They also use these models to identify the sources of the detected gravitational waves and determine their properties. How massive were the two black holes? Where and when did they merge? Did they merely orbit each other, or did they also spin around their own axes? How fast were they rotating, and around which axes? If researchers can answer these questions using precise waveform models, they can decipher how the black holes formed. They can also put Einstein's general theory of relativity to increasingly rigorous tests.
To detect and understand these signals, scientists need not only highly sensitive laser interferometers but also precisely tailored waveform models. These mathematical predictions provide the templates that researchers use to identify the signals in the observational data.
They also use these models to identify the sources of the detected gravitational waves and determine their properties. How massive were the two black holes? Where and when did they merge? Did they merely orbit each other, or did they also spin around their own axes? How fast were they rotating, and around which axes? If researchers can answer these questions using precise waveform models, they can decipher how the black holes formed. They can also put Einstein's general theory of relativity to increasingly rigorous tests.
The next generation of gravitational-wave detectors and waveform models
A new era is dawning for gravitational-wave astronomy in the coming decade. The LISA detector in space is designed for low-frequency gravitational waves that cannot be detected from the ground. At the same time, the planned 'third-generation' ground-based detectors — the Einstein Telescope and Cosmic Explorer — will observe gravitational waves similar to those detected by current instruments. However, these detectors will be up to ten times more sensitive in their final design and will capture a large number of very long and very loud signals.
The waveform models must also become significantly more accurate so that researchers can correctly interpret the data. “Our waveform models must be around 100 times more accurate than the current models,” says Jan Steinhoff, group leader in the Astrophysical and Cosmological Relativity department at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute; AEI) in the Potsdam Science Park. “Only with such precise theoretical models can we fully exploit the potential of the new observatories and gain new insights into the universe.”
The waveform models must also become significantly more accurate so that researchers can correctly interpret the data. “Our waveform models must be around 100 times more accurate than the current models,” says Jan Steinhoff, group leader in the Astrophysical and Cosmological Relativity department at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute; AEI) in the Potsdam Science Park. “Only with such precise theoretical models can we fully exploit the potential of the new observatories and gain new insights into the universe.”
Complex mathematics for a precision record
As a first step towards developing such highly precise waveform models, the researchers have focused on the initial phase of the merger. During this phase, two black holes orbit each other at a greater distance, emit gravitational waves and slowly continue to draw closer. The effects of general relativity are still very small during this phase. Therefore, their motion can be described by post-Newtonian theory: This essentially adds corrections from Einstein's general theory of relativity to Newton's theory of gravity. Complex mathematical methods originally developed in particle physics are employed to continually refine these corrections, accounting for parameters such as the black holes’ intrinsic spin.
Calculating black holes? Try particle physics!
In their study, published recently in the journal Physical Review Letters, the scientists treat black holes as particles to describe the initial phase of the merger and the resulting gravitational waves, using post-Newtonian theory.
This enabled the scientists to make predictions on the motion of black holes around each other with unprecedented accuracy across the four fundamental forces: gravity, electromagnetism, the weak interaction and the strong interaction.
Raj Patil, a doctoral student at the AEI, explains: “We had to perform highly complex calculations to take this most difficult step towards the new waveform models. Never before have researchers been able to calculate fundamental interactions with such precision.” Patil adds: 'While there is still a lot of work ahead of us before we have the final waveform templates, we are now very confident that we will achieve our goal following this breakthrough.”
This enabled the scientists to make predictions on the motion of black holes around each other with unprecedented accuracy across the four fundamental forces: gravity, electromagnetism, the weak interaction and the strong interaction.
Raj Patil, a doctoral student at the AEI, explains: “We had to perform highly complex calculations to take this most difficult step towards the new waveform models. Never before have researchers been able to calculate fundamental interactions with such precision.” Patil adds: 'While there is still a lot of work ahead of us before we have the final waveform templates, we are now very confident that we will achieve our goal following this breakthrough.”
Media contact:
Dr. Elke Müller
Press Officer AEI Potsdam, Scientific Coordinator
Tel: +49 331 567-7303
Email: elke.mueller@aei.mpg.de
Science Contacts:
Raj Patil
PhD Student
Tel: +49 331 567-7186
Email: raj.patil@aei.mpg.de
Dr. Jan Steinhoff
Group Leader
Tel: +49 331 567-7125
Email: jan.steinhoff@aei.mpg.de
Publication:
Brunello, G.; Mandal, M. K.; Mastrolia, P.; Patil, R.; Pegorin, M.; Ronca, J.; Smith, S.; Steinhoff, J.; Torres Bobadilla, W. J.
Six-loop gravitational interactions at the sixth post-Newtonian order. Physical Review Letters 137, 111401 (2026)
MPG.PuRe | | DOI | pre-print
Further information
Homepage of the “Astrophysical and Cosmological Relativity” Department
