When two black holes collide to form a new, larger black hole, they violently churn up space-time around them, sending out waves called gravitational waves in all directions. Previous studies of black hole collisions modeled the behavior of gravitational waves using what is known as linear mathematics, meaning that gravitational waves rippling outwards did not affect or interact with each other. Now, a new analysis has modeled the same precipitation in more detail, revealing so-called non-linear effects.
Nonlinear effects are what happens when waves crest a beach and crash,” says Keefe Mitman, a Caltech graduate student who works with Saul Teukolsky (PhD ’74), the Robinson Professor of Theoretical Astrophysics at Caltech with a joint appointment at Cornell University.
“he waves interact and influence each other rather than riding on their own. With something as violent as black hole mergers, we expected these effects, but so far we haven’t seen them in our models. New methods for extracting curves from our simulations made it possible to see nonlinearities.
The research, published in the journal Physical Review Letters, comes from a team of researchers from Caltech, Columbia University, Mississippi, Cornell University and the Max Planck Institute for Gravitational Physics.
In the future, the new model can be used to learn more about actual black hole collisions, which have been routinely observed by the Laser Interferometer Gravitational-wave Observatory (LIGO) since it made history in 2015 with the first direct detection of gravitational space waves. LIGO will turn on again later this year after receiving a set of improvements that will make the detectors even more sensitive to gravitational waves than before.
Supercomputers model how black holes evolve
Mitman and his colleagues are part of a team called Simulating eXtreme Spacetimes cooperation, or SXS. The SXS project, founded by Teukolsky in collaboration with Nobel laureate Kip Thorne (BS ’62), Richard P. Feynman Professor of Theoretical Physics, Emeritus, at Caltech, uses supercomputers to simulate black hole mergers.
Supercomputers model how black holes evolve as they spiral and coalesce 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 colliding black holes, which occurs right after two massive bodies merge.
“Supercomputers are needed to perform a precise calculation of the entire signal: the inspiration of two orbiting black holes, their merging and settling into a single quiescent remnant black hole,” says Teukolsky. “The linear treatment of the settling phase was the subject of my dissertation under Kip’s guidance some time ago. A new non-linear treatment of this phase will allow for more accurate wave modeling and possibly new tests of whether general relativity is in fact the correct theory of gravity for black holes.
The SXS simulations have proven helpful in identifying and characterizing the nearly 100 black hole smashups detected by LIGO so far. This new study represents the first time the team has identified nonlinear effects in simulations of the ringdown phase.
“Imagine there are two people on a trampoline,” says Mitman. “If they jump gently, they shouldn’t affect the other so much. This is what happens when we say that a theory is linear. But if one person starts bouncing with more energy, the trampoline will warp and the other person will start to feel their influence. This is what we mean by nonlinear: two people on a trampoline experience new oscillations due to the presence and influence of the other person.
In terms of gravity, this means that the simulations produce new types of waves. “If you dig deeper beneath the big waves, you’ll find another new wave with a unique frequency,” says Mitman. 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 says, “This is a big step in preparation for the next phase of gravitational wave detection that will deepen our understanding of gravity in these incredible phenomena taking place in the far reaches of space”.
