In 2015, astrophysicists for the first time detected gravitational waves, ripples in space-time that occur when neutron star or black hole mergers disrupt the cosmos. The observation of these waves confirmed Einstein’s theory of general relativity, which predicted such waves would occur if space-time worked as he believed it did. In the seven years since, nearly 100 merging black holes have been detected by observing the gravitational waves that these extraterrestrial events emit. Now, Caltech researcher Keefe Mitman and colleagues have modeled such collisions in more detail and revealed so-called nonlinear effects.

This artist’s conception shows a pair of supermassive black holes. Image credit: Josh Valenzuela, University of New Mexico.

“Nonlinear effects are what happens when waves on the beach crest and crash,” said Mitman, first author of a paper published in the journal Physical Review Letters.

“The waves interact and influence each other rather than ride along by themselves.”

“With something as violent as a black hole merger, we expected these effects but had not seen them in our models until now.”

“New methods for extracting the waveforms from our simulations have made it possible to see the nonlinearities.”

“In the future, the new model can be used to learn more about the actual black hole collisions that have been routinely observed by LIGO observatory ever since it made history in 2015 with the first direct detection of gravitational waves from space.”

Columbia University’s Professor Lam Hui used an analogy to describe the information that gravitational waves can provide:

“If I give you a box and ask you what’s in it, the natural thing to do is to shake it. That would tell you whether inside the box are candies or coins. That’s what we’re trying to do with these models, is gather a sense of the inner contents of a black hole by listening to the sound that’s emitted when it’s shaken.”

“The shaking in the case of black holes is the disruption that occurs when two collide and merge.”

“By listening to the harmonics that it emits, we can assess the space-time structure of the black hole.”

Mitman, Professor Hui and their colleagues are part of the Simulating eXtreme Spacetimes (SXS) Collaboration.

They use supercomputers to 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, they are 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,” said Caltech’s Professor Saul Teukolsky.

“The new nonlinear treatment of this phase will allow more accurate modeling of the waves and eventually new tests of whether general relativity is, in fact, the correct theory of gravity for black holes.”

The SXS simulations have proved instrumental in identifying and characterizing the nearly 100 black hole smashups detected by LIGO so far.

The new study represents the first time that the astrophysicists have identified nonlinear effects in simulations of the ringdown phase.

“Imagine there are two people on a trampoline. If they jump gently, they shouldn’t influence the other person that much. That’s what happens when we say a theory is linear,” Mitman said.

“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.”

In gravitational terms, this means that the simulations produce new types of waves.

“If you dig deeper under the large waves, you will find an additional new wave with a unique frequency,” Mitman said.

In the big picture, these new simulations will help researchers to better characterize future black hole collisions observed by LIGO and to better test Einstein’s general theory of relativity.

“This is a big step in preparing us for the next phase of gravitational-wave detection, which will deepen our understanding of gravity in these incredible phenomena taking place in the far reaches of the cosmos,” said Columbia University’s Dr. Macarena Lagos.

“We’re getting ourselves ready for when we’re going to be gravitational wave detectives, when we’ll be digging deeper to understand everything we can about their nature,” said University of Mississippi’s Professor Leo Stein.