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SXS—Simulating eXtreme Spacetimes—is a continuous scientific alliance that has been producing simulations of extraordinary occurrences in space, particularly the mergers of binary black hole systems, for multiple decades. Recently, SXS released a publication detailing version 3 of its binary black hole simulation catalog, six years following the unveiling of version 2.

In 2015, LIGO (the Laser Interferometer Gravitational-wave Observatory) successfully detected gravitational waves—ripples in space-time triggered by significant celestial occurrences—but the theoretical astrophysicists within the SXS collaboration had already dedicated two decades to forecasting what these waves might resemble as they arrived on Earth.

Gravitational waves emerge from various cosmic events, including mergers of neutron stars and black holes, traversing space and even penetrating the Earth. Highly sensitive instruments like LIGO capture the disturbances caused by these gravitational waves as they pass through and then endeavor to identify the type of celestial event that originated them. However, it’s equally crucial to approach this challenge from an alternate angle: by calculating the gravitational waveforms that would arise from different celestial phenomena before any detections are made. This is precisely the mission of the SXS collaboration.

Solving Einstein’s equations for merging black holes poses a significant challenge. “You can reformulate Einstein’s equations into a form categorized as hyperbolic, which is suitable for analyzing wave-like phenomena,” explains Keefe Mitman (PhD’24), currently a NASA fellow at Cornell University. “This indicates that if you provide these equations with specific initial data, a unique solution exists for how those data will progress over time. As we transition to higher-resolution outputs, we anticipate convergence: simulations that increasingly resemble the exact solution you would expect from Einstein’s equations.”

Presently, the scientists of SXS and LIGO exchange their data and equations back and forth, aligning predictions to observations and vice versa. As Mitman states, “we’re producing enough and LIGO is just starting to catch up. Until recently, when LIGO detected something, its astrophysicists would consult the SXS catalog to find a simulation that provides insights into their findings. If they cannot find what they require, they can request a new simulation from SXS with alternative parameters that may better correspond with their data.”

But who can foresee what lies ahead? During the 1970s and 1980s, theorizing about events like black hole mergers using a mathematical approach known as numerical relativity seemed more daunting than merely detecting gravitational waves as they reached Earth, and that endeavor appeared to be somewhere between highly challenging and entirely impossible. Nevertheless, in 50 years, gravitational-wave detection became a tangible reality.

In the future, data might outpace theory, prompting researchers of the SXS collaboration to persist in diligently theorizing the full range of potential black hole mergers. They produce the waveforms these occurrences would generate for gravitational wave detectors, which now include, along with LIGO, the Virgo interferometer near Pisa, Italy, and KAGRA (the Kamioka Gravitational Wave Detector), located in Gifu Prefecture, Japan, with future space-based interferometers like LISA (the Laser Interferometer Space Antenna) and DECIGO (the DECi-hertz Interferometer Gravitational wave Observatory) on the horizon. SXS then shares its models online, allowing anyone to, in a sense, retrieve a specific simulation and its accompanying computer code from the library shelf.

The newly issued expanded catalog is nearly double the size of its previous version: 3,756 simulations compared to the catalog from 2019. These simulations also consider a facet of gravitational waves predicted by general relativity but not previously included: gravitational-wave memory.

“Typically, when you envision waves, such as the expanding concentric waves created by tossing a rock in a pond, you know that after a while, the waves will dissipate and the pond’s surface will become flat once more,” Mitman states. “With gravitational waves, it differs slightly. When a gravitational wave traverses a certain area of space-time, that area expands and contracts in sync with the peaks and troughs of the gravitational wave. However, after the gravitational wave has passed, that space does not revert to its previous state. It undergoes a permanent transformation. That section of space-time retains a memory of the event, which is why we refer to it as the memory effect.”

With the gravitational-wave memory effect now incorporated into SXS’s simulations, theorists are nearing ever more accurate predictions for black hole mergers. “The catalog is extensively utilized by the global gravitational-wave community, with numerous papers citing it annually,” asserts Saul Teukolsky, the Robinson Professor of Theoretical Astrophysics. “For instance, waveform models used to search for events in LIGO data are calibrated against the highly precise simulations in the catalog. Additionally, theoretical concepts regarding general relativity can be evaluated against these simulations, which solve the precise equations of Einstein’s theory.”

“Black hole mergers can only be observed through gravitational waves,” Mitman clarifies, emphasizing that the efforts of SXS are crucial to advancing the frontiers of fundamental physics at the cosmic scale.

“The SXS Collaboration’s Third Catalog of Binary Black Hole Simulations” was published in Classical and Quantum Gravity. The initiative received backing from the National Science Foundation, NASA, and the European Union’s ERC Advanced Grant via the Max Planck Institute.

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