Solving general relativity equations for colliding black holes

Still image from animation of the inspiratory of a binary black hole with a mass ratio of 128: 1 showing the beginning of the last outbreak of gravitational waves. Photo credit: Carlos Lousto, James Healy, RIT

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

As early as the 1960s, physicists began using supercomputers to find solutions to this notoriously difficult problem. In 2000, with no solutions in sight, Kip Thorne, Nobel Prize winner 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 groups at NASA and Caltech-derived independent solutions.)

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

“It took us two weeks to realize that this really came from nature and not from entering our simulation as a test,” said Lousto, now professor of mathematics 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 merging of two black holes. ”

Lousto is back with a new milestone in numerical relativity and this time simulates the merging of black holes, where the ratio of the mass of the larger to the smaller black hole is 128 to 1 – a scientific problem at the limit of what is computationally possible. His secret weapon: the Frontera supercomputer at TACC, the eighth most powerful supercomputer in the world and the fastest at every 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 nonetheless serves as the computing power that will help advance the field of astrophysics.

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

LIGO can only detect gravitational waves caused by small holes of medium and medium mass of approximately the same size. Observatories will be 100 times more sensitive to spot the kind of fusions Lousto and Healy modeled. 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 ultimate merged black hole, including its final mass, spin, and recoil velocity. This led to some surprises.

“These fused black holes can have speeds that are much greater than previously known,” said Lousto. “You can travel at 5,000 kilometers per second. You emerge from a galaxy and wander through the universe. That’s another interesting prediction. ”

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

Previously, the largest mass ratio ever solved with high precision was 16 to 1 – eight times less extreme than Lousto’s simulation. The challenge in simulating larger mass ratios is that the dynamics of the interacting systems must be resolved 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 to refine the areas of the mesh where it is needed in more detail.

Lousto’s team approached the problem with a methodology that he compares to Zeno’s first paradox. By halving and halving the mass ratio while adding internal lattice refinement stages, they were able to switch from 32: 1 mass ratios of the black holes to 128: 1 binary systems that go through 13 orbits prior to merging. It took seven months of constant calculation on Frontera.

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

The 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 fusion. Lousto would like to solve the equations eleven more times in order to get a good first range of possible “templates” that can be compared with future detections.

The results will help the designers of future earth- and space-based gravitational wave detectors to plan their instruments. These include advanced third-generation ground-based gravitational wave detectors and the laser interferometer space antenna (LISA), which is expected to be launched in the mid-2030s.

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

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

Reference: “Exploring the binary black hole fusion with a small mass ratio via Zeno’s dichotomy approach” by Carlos O. Lousto and James Healy, November 5, 2020, Physical Examination Letters.
DOI: 10.1103 / PhysRevLett.125.191102