Ringing black holes are the result of a phenomenon known as “ringdown,” which occurs after the merger of two black holes or the perturbation of a single black hole. When a black hole is disturbed, gravitational waves are produced that propagate through spacetime, causing the black hole to “ring” or vibrate as it settles into a stable state.

A new study detailed the modeling of black hole collisions and discovered so-called nonlinear effects within gravitational waves. Nonlinear effects occur ‘when waves on the beach crest and crash.’

When two black holes collide to form a new larger black hole, they violently roil spacetime around them, causing ripples known as gravitational waves to spread out in all directions. Previous studies of black hole collisions used linear math to model the behavior of the gravitational waves, which means that the gravitational waves rippling outward had no influence or interaction with each other. A new analysis has now modeled the same collisions in greater detail, revealing so-called nonlinear effects.

“Nonlinear effects are what happens when waves on the beach crest and crash,” says Keefe Mitman, a Caltech graduate student who works with Saul Teukolsky (Ph.D. ’74), the Robinson Professor of Theoretical Astrophysics at Caltech and Cornell University. “Rather than riding alone, the waves interact and influence one another. We expected these effects with something as violent as a black hole merger, but we hadn’t seen them in our models until now. Nonlinearities can now be seen thanks to new methods for extracting waveforms from our simulations.”

Nonlinear effects are what happen when waves on the beach crest and crash. Rather than riding alone, the waves interact and influence one another. We expected these effects with something as violent as a black hole merger, but we hadn’t seen them in our models until now.

Keefe Mitman

The research, published in the journal Physical Review Letters, come from a team of researchers at Caltech, Columbia University, University of Mississippi, Cornell University, and the Max Planck Institute for Gravitational Physics.

The new model can be used to learn more about the actual black hole collisions that LIGO (Laser Interferometer Gravitational-wave Observatory) has routinely observed since it made history in 2015 with the first direct detection of gravitational waves from space. LIGO will reactivate later this year following a series of upgrades that will make the detectors even more sensitive to gravitational waves than before.

Mitman and his colleagues are part of a team called the Simulating eXtreme Spacetimes collaboration, or SXS. Founded by Teukolsky in collaboration with Nobel Laureate Kip Thorne (BS ’62), Richard P. Feynman Professor of Theoretical Physics, Emeritus, at Caltech, the SXS project uses supercomputers to simulate black hole mergers. The supercomputers model how the black holes evolve as they spiral together and merge using the equations of Albert Einstein’s general theory of relativity. In fact, Teukolsky was the first to understand how to use these relativity equations to model the “ringdown” phase of the black hole collision, which occurs right after the two massive bodies have merged.

“Supercomputers are needed to carry out an accurate calculation of the entire signal: the inspiral of the two orbiting black holes, their merger, and the settling down to a single quiescent remnant black hole,” Teukolsky says. “A long time ago, I wrote my Ph.D. thesis under Kip on the linear treatment of the settling down phase.” The new nonlinear treatment of this phase will allow for more accurate wave modeling and, eventually, new tests to determine whether general relativity is the correct theory of gravity for black holes.”

SXS simulations have been critical in identifying and characterizing the nearly 100 black hole smashups detected by LIGO thus far. This new study represents the first time that the team has identified nonlinear effects in simulations of the ringdown phase.

“Imagine there are two people on a trampoline,” Mitman says. “If they jump gently, they shouldn’t influence the other person that much. That’s what happens when we say a theory is linear. But if one person starts bouncing with more energy, then the trampoline will distort, and the other person will start to feel their influence. This is what we mean by nonlinear: the two people on the trampoline experience new oscillations because of the presence and influence of the other person.”

This means that the simulations generate new types of gravitational waves. “If you dig deeper beneath the large waves, you’ll find another new wave with a distinct frequency,” Mitman says.

In the long run, these new simulations will help researchers better characterize future LIGO black hole collisions and test Einstein’s general theory of relativity.