A new cosmic model to reveal what’s inside colliding black holes

An artist’s impression of two black holes colliding and merging. New research has led to the development of a more sophisticated model for modeling cosmic events, which will allow for a deeper understanding of the structure of merging black holes.

A research paper uses new methods to analyze the waves that black holes emit when they collide.

In 2015, scientists first detected gravitational waves, ripples in space-time that occur when large cosmic events—like the collision and merger of two black holes—disrupt the cosmos. The observation of these waves confirmed Einstein’s theory of general relativity, which predicted that such waves would occur if spacetime worked as he believed it did. In the seven years since, nearly 100 merging black holes have been discovered by observing gravitational waves that these extraterrestrial events emit.

Now, thanks to new research, the ability to model these cosmic events has become more sophisticated. The team of 14 researchers was led by Caltech PhD student and Columbia College alum Keefe Mitman (CC’19), Columbia postdoc Macarena Lagos, Columbia Professor Lam Hui, and University of Mississippi Professor Leo Stein. The improved model they developed paves the way for a deeper understanding of the structure of black hole mergers.

In “Nonlinearities in Black Hole Ringdowns,” a new paper published in Physical review letters, the team outlines a more complex way to model the signal that gravitational waves emit by including nonlinear interactions in the models. This modeling approach will allow scientists to better understand the structure of what happens inside black holes, and will also help test whether Einstein’s general theory of relativity correctly describes the behavior of gravity in extreme astrophysical environments.

Two black holes merging computer rendering

A computer rendering of two black holes that are about to merge, seen from above. Credit: SXS Lensing/Simulating eXtreme Spacetimes Collaboration

“This is a big step in preparing us for the next phase of gravitational wave detection, which will deepen our understanding of gravity and these incredible phenomena that take place far out in the cosmos,” said Lagos, a co-author on the paper.

The research comes at an appropriate time: in March, LIGO, the observatory that first detected gravitational waves, will be powered up to gather new observations of events taking place far out in space. The observatory has not operated since 2020, when it was closed due to the pandemic. Several other larger detectors are expected to begin collecting data in the coming years, making it even more important that they have sophisticated models to interpret incoming information.

Co-author 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 shake it. That would tell you if there’s candy or coins in the box. That’s what we’re trying to do with these models is to gather a sense of the inner contents of a black hole by listening to the sound emitted when it is shaken.” The “shake” in the case of black holes is the disturbance that occurs when two collide and merge. “By listening to the harmonics that it emits, one can we assess the space-time structure of the black hole.”

Models of gravitational waves emitted after the merger of two black holes have so far only included linear interactions, which work well and provide valuable information about the structure and content of black holes. However, this new model could offer as much as a 10% improvement in overall numbers accuracy of black hole models, the paper’s authors said.

To understand the importance of using non-linearity to describe gravitational waves, the authors described waves in an ocean: A wave that rises and falls without splashing water into the air could be described by a linear equation. But a cresting and breaking wave exhibits non-linear interactions: while some water swells at the base of the wave, other water simultaneously crashes left, right, up and down in tendrils and water droplets above it. A nonlinear model of the wave will allow you to understand how and when all the water in the wave, including the airborne droplets, moves. Gravitational waves are similar to water waves, and the new model is able to account for the extraterrestrial equivalent of extra water droplets.

“We’re getting ready for when we’ll be gravitational wave detectives, when we’ll dig deeper to understand everything we can about their nature,” said Stein, one of the paper’s authors.

Reference: “Nonlinearities in Black Hole Ringdowns” by Keefe Mitman, Macarena Lagos, Leo C. Stein, Sizeng Ma, Lam Hui, Yanbei Chen, Nils Deppe, François Hébert, Lawrence E. Kidder, Jordan Moxon, Mark A. Scheel, Saul A. Teukolsky, William Throwe and Nils L. Vu, 22 February 2023, Physical review letters.
DOI: 10.1103/PhysRevLett.130.081402

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