Ever since LIGO (and now Virgo) started picking up gravitational waves, theorists have gone nuts. The volume of papers on exciting possibilities seems to grow faster than the disk space available to accommodate them. If I were sensible, I would probably ignore them. But I'm not, and you, dear reader, will suffer along with me.

When two black holes collide and merge, they emit gravitational waves, but we don't expect them to emit light. But is that really true? After all, black holes decay away by emitting Hawking radiation, so maybe there is some light associated with the event.

How black are we talking?

Now, it should be pointed out that Hawking radiation, though widely accepted as an inevitable consequence of black hole physics, has never been observed. The problem is that big, long-lived black holes emit tiny amounts of Hawking radiation at very long wavelengths. The low intensity, combined with the long wavelength, makes it pretty much impossible to detect. Tiny, short-lived black holes are much brighter and might be detectable... but, I'm not sure that anyone has any idea how such a black hole might be formed in the present-day Universe. Every black hole we know about is in the large and long-lived bucket.

So, under ordinary circumstances, black holes are, for all practical purposes, black.

But, a black hole collision is anything but ordinary. And researchers are starting to wonder if there might be some glow associated with the collision. Investigating the emission of Hawking radiation during in-spiral and collision turns out to be quite tricky, though. As two black holes spiral together, they move at a respectable fraction of the speed of light. Solving the equations of general relativity for this system already requires a lot of heavy lifting with computers—and that doesn't include adding on the bits that involve Hawking radiation.

But, as with all things, you have to start somewhere. So a group of researchers chose to examine some of the details of Hawking radiation immediately after a black hole merger. Just after the collision, the merged black hole emits a few more gravitational waves as it relaxes. In fact, the best analogy is the ringing of a bell. Our cosmic bell is the event horizon, which squeezes and expands as it absorbs and emits gravitational waves.

The researchers cobbled together a model that examines the phase and amplitude of Hawking radiation in relation to the gravitational waves that the black hole produces.

The light of ringing space

The findings can be summarized as follows: the oscillations of the black hole modulate the phase and amplitude of Hawking radiation. Essentially, at those moments in time when a gravitational wave is being absorbed, light can be emitted. Under ordinary circumstances, Hawking radiation looks like thermal radiation, which basically means it has the same properties as the light emitted from an incandescent bulb (although in a different part of the electromagnetic spectrum). That means that no two photons from a black hole share much in common: phase, amplitude, direction are all randomly selected for each photon.

But the periodic oscillations of the black hole give these photons correlations, making it unlike an incandescent bulb. In fact, the researchers show that the photons are what physicists call squeezed.

Squeezing involves the fact that the phase and amplitude of a photon are governed by the uncertainty principle; they cannot both be defined to arbitrary precision. A squeezed photon is one in which either the amplitude or phase is defined to a precision that is better than the joint minimum, while the other property is much noisier. Nothing we're aware of naturally emits squeezed light. It usually takes highly specialized circumstances to get non-classical light sources like squeezed-photon emitters.

This means that oscillating black holes may be our first example of naturally occurring emitters of squeezed light. And, even better, the absorption of gravitational waves by the black hole amplifies the Hawking radiation.

Black holes: A sound and light show?

This all sounds pretty exciting, so should we be searching the night sky for squeezed radio waves? Well, there is some way to go yet before researchers start asking for telescope time.

The problem is that this analysis is limited to the ring-down of the black hole. The amplification of Hawking radiation is proportional to the duration of the ring-down, which lasts just a few milliseconds. Or, to put it in hard numbers: GW150914, the first merger LIGO observed, might have had a ring down that was long enough to emit one or two squeezed photons.

What makes this interesting is that, during the in-spiral before the collision, there are long-lasting oscillations. If the researchers' analysis scales in the same way (meaning the details are different, but the general picture remains the same), then the number of photons would go up dramatically. The researchers predict that a mode that lasts on the order of 30 milliseconds might emit around 1042 photons. I put that at about 1016W of radio waves, which sounds like a lot but is still tiny compared to the Sun's 1026W.

That last comparison is not entirely fair, though, because the researchers calculate the energy emitted by coupling to a single gravitational wave mode (radiation comes in modes that define their characteristics). During in-spiral, many modes will be excited, and the in-spiral will last somewhat longer than 30 milliseconds (although we only care about the very end, where the gravitational wave amplitude is huge). So it might not be beyond the bounds of possibility to detect these emissions.

I know that I and many others often get impatient with theoretical physicists predicting stuff that we are unlikely to measure. But we need to rein in our impatience somewhat. The cool thing about being a theoretical physicist, especially in some areas, is that your imagination is the limit. In fact, I'd say that a well-cultured imagination is a drawback.

A good theoretician's imagination seems to be a fetid, steaming swamp, filled with the buzzing insects of quantum mechanics, the alligators of general relativity, the floating islands of Newtonian mechanics, and, yes, the occasional unidentified, half-seen scaly beast. Without theoreticians chasing down these half-seen beasts and imagining more things than are actually there, we will never know how to look for anything in the swamp, much less find anything.

So, even though I am skeptical that the radiation from colliding black holes is detectable (if it even exists), this is still a really nice result. For the first time, it seems to imply that a big black hole might emit enough Hawking radiation to be detectable, and that is worth a second look.

Physical Review D, 2017, DOI: 10.1103/PhysRevD.96.065017