Can one hear the shape of a black hole? [*]

[Edit: see also the Synopsis in APS Magazine "Physics", the coverage and this interview (in Italian) by the Italian Institute for Astrophysics (INAF), and the stories in Physics World, NewScientist, Phys.org, Le Monde and Repubblica.]


An orchestra conductor can easily tell a gong from a bell just by their different sound. Can astronomers do the same and tell a black hole from another dark object just by detecting their different gravitational-wave signal? In our recent paper, Vitor Cardoso, Edgardo Franzin and I show that this might not be the case [preprint here].


Last February, the LIGO/Virgo Collaboration announced the first direct detection of gravitational waves by the two laser interferometers advanced LIGO. This historical discovery has been also welcomed as the first conclusive proof for the existence of black holes, the most extreme objects in the Universe. The detected signal --dubbed GW150914-- corresponds to the "pas de deux" of two massive objects, which inspiral around each other and eventually collide in a cosmic spacetime-quake. LIGO data firmly show that the two objects are extremely compact and way too massive to be neutron stars. While providing compelling evidence, this does not represent a bullet-proof confirmation of the existence of black holes by itself. After all, signatures of compact, dark and massive objects come routinely from electromagnetic observations with infrared and X-ray detectors.

What makes GW150914 really unique is that the gravitational-wave signal contains all the final stages of the cosmic evolution of the binary system: the two objects lose an enormous amount of energy through the emission of gravitational waves, approach each other and eventually merge to form a single compact object of about 62 solar masses. After the merger (which lasted only a few milliseconds!) the final object was highly distorted and underwent an adjustment phase known as the "ringdown", in which the object vibrates pretty much like a drum. Just like the notes of the drum depend on its properties (the shape, the size, the material), the "ringdown modes" should carry information about the very nature of the final object produced after the merger.

A comparison between the ringdown signal of a particle falling into a black hole (black dashed line) and the same particle falling into a wormhole (red line). The wormhole geometry is illustrated in the top right corner. The two signals are identical at early times and the "universal" ringdown waveform is associated to the particle reaching point "A" (the light ring). The real quasinormal modes of the wormhole appear only at late times, when the particle reaches the throat (point "B").

Black holes are snatches in the spacetime fabric and their rim ---known as the event horizon--- vibrates in a very peculiar way that was predicted after decades of restless work by using Einstein's theory of general relativity. Scientists hope that, by detecting events like GW150914, one would be able to identify the modes of vibration of the final black hole (the so-called "quasinormal modes") from the ringdown signal. Detecting the quasinormal modes will be the definitive proof that black holes are produced in a binary merger, precisely as predicted by Einstein's theory.


In our recent work (selected as an Editor's Suggestion and featuring the cover of the current issue of Physical Review Letters), we show that this paradigm is incorrect. The vibrations of very compact objects without an event horizon are dramatically different from those of black holes (their frequency is lower and they last much longer time) and, nonetheless, the ringdown signal produced by these "black-hole mimickers" is identical to that of a black hole.




We studied the ringdown of a "wormhole", a tunnel through spacetime connecting two distant regions of the universe. This hypothetical object (also featuring in the movie "Interstellar") is predicted by general relativity in the presence of exotic forms of matter. A wormhole is intrinsically different from a black hole in that it does not possess an event horizon.

The ringdown of such wormhole can be almost identical to that of a black hole and that a putative event horizon would leave a trace in the gravitational waveform only at very late times, when the signal is probably too small to be detectable.

"This is not a black hole." is what Rene' Magritte would probably say about the ringdown waveform.
[Credits: Ana Sousa Carvalho]

Thus, just like our orchestra conductor should have an extremely acute musical ear to tell the difference between two drums playing almost the same note, gravitational-wave detectors need to be extremely sensitive to the final ringdown, where the real nature of the final object eventually shows up.

With the improved sensitivity that gravitational-wave interferometers will reach in the next years, events like GW150914 can provide a unique opportunity to test quantum effects near the event horizon. If the final word can be put on the nature of black holes, this will definitely come from gravitational waves.




[*] "Can One Hear the Shape of a Drum?" is the title of a famous work by Marc Kac, where he discusses an old conjecture that the shape of a drum can be inferred solely from its sound.