Solving general relativity equations for the collision of black holes

Solving the equations of general relativity for the collision of black holes is not an easy thing.

As early as the 1960s, physicists began to use supercomputers to find solutions to this notoriously difficult problem. In 2000, with no solutions in sight, Kip Thorne, Nobel Prize 2018 and one of the designers of LIGOI bet there would be an observation of Gravitationswellen before a numerical solution has been reached.

He lost that bet when Carlos Lousto, then at the University of Texas at Brownsville, and his team developed a solution using the Lonestar supercomputer at the Texas Advanced Computing Center in 2005. (At the same time, the groups of NASA and independent solutions derived from Caltech.)

When the Laser Interferometer Gravitational Wave Observatory (LIGO) first observed such waves in 2015, Lousto was in shock.

“It took us two weeks to realize that this really came from nature and not from coming into our simulation as a test,” said Lousto, now a math professor at the Rochester Institute of Technology (RIT). “The comparison with our simulations was so obvious. They could see with their naked eyes that it was the merger of two black holes. ”

Lousto is back with a new milestone in numerical relativity and this time it simulates the merger of black holes, where the ratio of the mass of the largest to the smallest black hole is 128 to 1 – a scientific problem bordering on what it is. computationally possible. Its secret weapon: the Frontera supercomputer at TACC, the eighth most powerful supercomputer in the world and the fastest in any university.

His research with collaborator James Healy, supported by the National Science Foundation (NSF), was published in Physical examination letters this week. It may take decades to confirm the results experimentally, but it still serves as a computing power that will help advance the field of astrophysics.

“Modeling pairs of black holes with very different masses is very challenging from a computational point of view because they must be maintained precision in a variety of grid resolutions, “said Pedro Marronetti, Program Director for Gravitational Physics at NSF.” The RIT group has performed the world’s most advanced simulations in this area, and each of them brings us closer to understanding observations that gravitational wave detectors will provide in the near future “.

LIGO is able to detect only gravitational waves caused by small holes of medium and medium mass of approximately the same size. Observers will be 100 times more sensitive to detect the type of fusion modeled by Lousto and Healy. Their results reveal not only what the gravitational waves caused by a 128: 1 fusion would look like to an observer on Earth, but also the properties of the last molten black hole, including its final mass, spin, and recoil velocity. This led to some surprises.

“These fused black holes can have much greater velocities than previously known,” Lousto said. “You can travel at 5,000 kilometers per second. Get out of a galaxy and roam the universe. This is another interesting prediction. ”

The researchers also calculated the gravitational waveforms – the signal that would be detected near Earth – for such mergers, including the peak frequency, amplitude and brightness. When these values ​​were compared with the predictions of existing scientific models, their simulations were within 2% of the expected results.

Previously, the largest mass ratio ever solved with high precision was 16 to 1, eight times less extreme than the Lousto simulation. The challenge in simulating larger mass ratios is that the dynamics of interacting systems must be solved in additional scales.

Like computer models in many fields, Lousto uses a method called adaptive mesh refinement to obtain precise models of the dynamics of interacting black holes. The point is to put the black holes, the space between them and the distant observer (us) on a grid or mesh and refine the areas of the mesh where it is needed in more detail.

Lousto’s team approached the problem with a methodology that compares to Zeno’s first paradox. By halving and halving the mass ratio and adding internal lattice refinement steps, they were able to shift from 32: 1 mass ratios of black holes to 128: 1 binary systems that traverse 13 orbits before merging. It took seven months of constant calculations on Frontera.

“Frontera was the perfect tool for the job,” Lousto said. “Our problem requires high performance processors, communications and memory, and Frontera has all three.”

Simulation is not the end of the road. Black holes can have a variety of rotations and configurations that affect the amplitude and frequency of the gravitational waves produced by their merger. Lousto would like to solve the equations eleven more times in order to obtain a good first range of possible “models” that can be compared with future findings.

The findings will help designers of future ground and space gravitational wave detectors plan their instruments. These include ground-based advanced third-generation gravitational wave detectors and the laser interferometer (LISA) space antenna, which is expected to be launched in the mid-1930s.

Research can also help solve basic black hole puzzles, such as how some can get so large – a million times the mass of the sun.

“Supercomputers help us answer these questions,” Lousto said. “And the problems inspire new research and pass the baton to the next generation of students.”

Reference: “Exploring Binary Black Hole Fusion with a Small Mass Ratio Using Zeno’s Dichotomous Approach” by Carlos O. Lousto and James Healy, 5 November 2020, Physical exam letters.
DOI: 10.1103 / PhysRevLett.125.191102