A collision with a black hole generates a new larger black hole. The collision violently shakes spacetime, sending ripples called gravitational waves outward in all directions.

Previous research on black hole collisions analyzed the behavior of gravitational waves using linear math, implying that the gravitational waves that rippled outward were independent. Now, new research has more accurately modeled the same collisions and revealed so-called nonlinear effects.

When waves collide with the beach crest, non-linear effects occur. Instead of traveling in isolation, the waves interact and influence each other.

Keefe Mitman, a Caltech graduate student working with Saul Teukolsky (Ph.D. ’74), said: “We anticipated these effects with something as violent as a black hole merger, but we had not yet observed them in our simulations. The waveforms from our simulations can now be extracted using new techniques, making it possible to detect the non- observing linearities.”

In the future, the new model can be used to learn more about the actual black hole collisions routinely observed by LIGO (Laser Interferometer Gravitational-wave Observatory) in 2015.

A group called the Simulating eXtreme Spacetimes Collaboration, or SXS, includes Mitman and his colleagues. The SXS project, started by Teukolsky in collaboration with Nobel laureate Kip Thorne (BS ’62), emeritus Richard P. Feynman, professor of theoretical physics at Caltech, simulates black hole mergers using supercomputers.

Using the equations from Albert Einstein’s general theory of relativity, supercomputers simulate how black holes evolve as they spiral and merge together. Teukolsky was the first to realize how these equations of relativity could be used to simulate the “ringdown” phase of the black hole collision, which occurs immediately after the two massive entities merge.

ringdown phase of a black hole
This illustration shows the ringdown phase of a black hole recently created by the collision of two smaller black holes. A new model for this phase of black hole merger shows the previously known linear effects (blue) and the newly discovered nonlinear effects (orange). The nonlinear effects, which have their own unique frequency, are created by the linear effects near the black hole’s light ring before escaping in the form of gravitational waves. Credits: L. Stein (University of Mississippi)/K. Mitman (Caltech)

Teukolsky said: “It takes supercomputers to perform an accurate calculation of the entire signal: the inspiration source of the two orbiting black holes, their merging and precipitating into a single, resting black hole remnant. The linear treatment of the settlement phase was the subject of my PhD. thesis under Kip a while ago. The new non-linear treatment of this phase will allow more accurate modeling of the waves and ultimately new tests to verify whether general relativity is indeed the correct theory of gravity for black holes.”

The approximately 100 black hole mergers that LIGO has observed so far have all been identified and described, largely thanks to the SXS simulations. With this new study, the team has discovered nonlinear effects in ringdown phase simulations for the first time.

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

Co-author Macarena Lagos of Columbia University said: “This is a big step in preparing 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.”

Magazine reference:

  1. Keefe Mitman, Macarena Lagos et al. Nonlinearities in black hole ringdowns. Physical assessment letters. DOI: 10.1103/PhysRevLett.130.081402