Simulation of the black hole merger observed by LIGO known as GW150914. Credit: SXS, the Simulating eXtreme Spacetimes (SXS) project |

When two black holes collide into each other to form a new bigger black
hole, they violently roil spacetime around them, sending ripples, called
gravitational waves, outward in all directions. Previous studies of black
hole collisions modeled the behavior of the gravitational waves using what
is known as linear math, which means that the gravitational waves rippling
outward did not influence, or interact, with each other. Now, a new analysis
has modeled the same collisions in more detail and revealed 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 with a joint appointment at Cornell University.

"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."

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

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 (Laser
Interferometer Gravitational-wave Observatory) ever since it made history in
2015 with the first direct detection of gravitational waves from space. LIGO
will turn back on later this year after getting a set of upgrades that will
make the detectors even more sensitive to gravitational waves.

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. "The linear treatment of the settling down phase was the subject of my
Ph.D. thesis under Kip quite a while ago. 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.
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."

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 says.

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.

Says co-author Macarena Lagos of Columbia University, "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."

### Reference:

Keefe Mitman et al, Nonlinearities in black hole ringdowns, Physical Review
Letters (2023). Accepted for publication:
journals.aps.org/prl/accepted/ … 5c5aaa672c0e199adcff. On Arxiv:
DOI: 10.48550/arxiv.2208.07380

Tags:
Space & Astrophysics