Atoms of different elements have distinct spectra. Atomic spectroscopy has been used to identify different elements and to discover new elements by observing their electromagnetic emission spectra. We are now on the verge of doing the same with gravitational waves.
“Black hole spectroscopy” was studied theoretically for about 50 years. According to general relativity, when two black holes collide they merge and form a perturbed black hole that emits gravitational waves at very specific frequencies. The remnant of these mergers “rings down” like a bell. The observational data from gravitational wave detectors can put these predictions to the test. For the black hole mergers observed by LIGO and Virgo, the “ringdown” has a frequency of about a kilohertz or smaller, and dies out within a millisecond. Black holes die out quickly!
However, most of these predictions were based on the linear approximation of Einstein’s theory of general relativity. The linear approximation ignores strong gravity effects that should be present when black holes collide, yet the merger looks surprisingly linear. Where did all the nonlinearities go?
In a paper led by Mark Cheung, published in Physical Review Letters as an Editors’ Suggestion and discussed (together with a companion paper by Mitman et al.) in this Physics Viewpoint by Swetha Bhagwat, we discovered that, before going quiet, the “sounds” emitted by black holes actually carry imprints of the full, nonlinear Einstein equations, and allow us to test Einstein’s theory in all its glory.
To come to these conclusions, we studied very carefully two sets of numerical simulations: the “quasicircular” mergers observed by LIGO/Virgo (studied also by Mitman et al.) and the head-on collision of two black holes close to the speed of light, where gravity is strongest - see this Johns Hopkins press release by Roberto Molar Candanosa, with a nice video of ultrarelativistic collisions produced by Thomas Helfer.
The simulations imply that nonlinearities might be observable with future gravitational-wave detections. Black hole spectroscopy is a newborn field and it can be used to understand in depth how black holes ring, and the inner workings of Einstein’s theory of general relativity.
