Building Black Holes (Script) (Patreon)

Black holes are very real, but our understanding of them remains highly theoretical. If only we could build one in the lab. Oh wait, we can.

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Black holes are about the worst subjects for direct study in the universe. First there’s the whole thing about never being able to see inside one beneath the inescapable event horizon. Then there’s the fact that real black holes are, thankfully, very far away and on cosmic scales very tiny. It took a telescope the size of the planet to be able to make an image of the nearest gigantic one. Nonetheless, the evidence for their reality is overwhelming. Stars orbiting in crazy slingshots around a patch of nothingness in the center of our galaxy, superheated disks of gas pouring into tiny spaces in quasars or X-ray binary systems. Gravitational waves that perfectly match our theoretical prediction for black hole mergers. And, again, this picture of the black hole at the heart of a galaxy over 50 million light years away.

But at this stage, it’s all we can do to convince ourselves of their existence. Actually studying the physics of real black holes is much, much harder. I mean, we could try to make one - but that’s way beyond our current tech level, and also potentially humanity-destroying. Well it turns out we don’t need to make real black holes to at least get started with the lab work. We can instead study analog black holes - and by analog, I don’t mean old fashioned clockwork black holes - I mean analogies. Physical systems that aren’t black holes but that behave in similar ways - and may reveal the real behaviours of real black holes.

The whole idea of analog black holes was started in 1972 by Bill Unruh - most famous for his Unruh radiation, which we’ve talked about before. Now Bill Unruh did work with actual analog black holes, but it first started with a pure thought experiment. 

It goes like this: Imagine you’re a blind fish living in a river. If the river isn’t moving, sound propagates in all directions equally. Normally you can explore your world by listening to sounds upstream and downstream—because the speed of the river is slower than the speed of sound in the water. But at a certain place in the river, you know that there’s a waterfall. It’s not a normal waterfall, but a waterfall so powerful that the speed of the falling water exceeds the speed of sound in that water. So what happens if another fish goes over the waterfall? Since sound waves are just vibrations propagating through a medium, if the medium is traveling faster than the vibrations in the opposite direction, the sound will never reach you. In other words, the water drags the sound made by the other fish so fast it can never reach you. 

Just replace sound with light and the water with spacetime itself and you have a black hole. The surface around the central, massive point where the waterfall of space equals the speed of light is our event horizon. No information - from fish or astronauts or anything - can reach us from beneath that surface. 

At first Unruh thought that this was just an illustrative, evocative example of the power of event horizons. But by 1982 he realized the two situations had much more in common, mathematically speaking. It turns out that the equations of fluid dynamics can be expressed in a form that is a close analogy to the equations governing the flow of spacetime - the equations of general relativity, And a vortex expressed in those equations of fluid flow resembles a black hole - right down to the emission of Hawking radiation. The details are a bit dense for YouTube, but I’ll link a lovely paper by Matt Visser for those who want to delve into the math.

Over the years, physicists have capitalized on these kinds of mathematically analogous situations and found a number of systems with event horizons 

Analog theoretical black holes are all very well, but their real value is that they tell us we might be able to build analog black holes in the lab. There are some extremely interesting high tech examples I’ll come back to … But even now, some of the most instructive efforts use the same medium as Bill Unruh’s thought experiment - black holes made of water.

One setup uses a tank in which a current of water flows over a sloped obstacle. As the depth of water decreases, the current accelerates while the speed of surface waves slows down. At some point the flow is faster than the waves - and that’s your analog event horizon. If the flow is in the opposite direction to the waves this is actually an analog white hole. Other experiments use a carefully-shaped hole in a tank to create a classic vortex - in fact, the technical term is bathtub vortex. When the downward flow of water reaches the speed of ripples on the tank surface you again have an analog event horizon. 

At these event horizons, physicists can look for black hole-like behavior. For example, Hawking radiation. All the gory details of hawking radiation are in our previous episode, but let’s review. In 197. Stephen Hawking predicted that real black holes would, contrary to prior thought, leak away their mass as a type of radiation. The popular description is that pairs of virtual particles appear near the event horizon and are separated - one escapes and one falls in, somehow converting to negative energy and so decreasing the mass of a black hole. A more technical description involves the black hole scattering vibrational modes of the quantum fields that have wavelengths similar to the black hole’s event horizon. This perturbs the quantum fields in a way that look likes escaping particles if you’re very far from the black hole. 

So in the case of an analog watery black hole you just replace “vibration in quantum field” with “ripple on surface of water” and viola, same deal. Hopefully. 

And in fact Hawking-like radiation has been observed in these analog black holes. Or at least, the perturbations in the frequencies of the surface ripples have properties closely analogous to Hawking radiation. One aspect of Hawking radiation that can only be studied with analog black holes is what actually happens inside the black hole itself. The standard picture is that energy gets sapped from the black hole because the infalling particles-slash-vibrations themselves acquire negative energy. This effect on the black hole is called the backreaction of the Hawking radiation - and actually, it’s somewhat contentious exactly what happens here. In Hawking's own early papers, he totally glosses over the effect, essentially just saying that black holes must lose mass for the sake of energy conservation.

Well, now researchers think they’ve detected exactly the expected sapping of the “gravitational field” in a vortex black hole analog. In fact, both the analog of energy and angular momentum seem to be sapped by this Hawking-like radiation. 

Bathtub vortices are fantastic laboratories for spinning black holes in particular. Now we’ve looked deeply into rotating, or Kerr black holes recently. Very deeply in fact - we’ve traveled through them to other universes. Their physics is extremely speculative, but some of that physics is now on much more solid footing based on experiments with a tank of water. 

One thing we saw was that rotating black holes can donate some of their rotational energy to particles or waves that pass close by. This is the Penrose process, and when the particle being boosted is light then we call it superradiance. So this works when the particle passes through the black hole’s ergosphere. That’s the region outside the event horizon where the circular flow of space become irresistible. It turns out that water vortices also have the ergo-regions, where surface ripples are dragged in circles. And vortices can also superradiate. 

Silke Weinfurtner demonstrated this in a brilliant analog black hole setup. It consists of a giant, 2000 litre tank of fluorescent water.. Water pours in from two sides, creating a slow rotation that eventually spins into a carefully shaped funnel, forming a whirlpool. A high speed camera captures all the action to great precision. On one side of the tank, a wave generator propagates waves across the surface where they pass across the whirlpool. These waves are analogous to incoming particles. The waves are only 1 millimeter high, but superradiance can increase their height by as much as 10%. 

As useful as classical analogs are, Hawking radiation is ultimately a quantum mechanical effect. Deeper insights may require an analog quantum black hole. Enter the Bose-Einstein condensate. Bose-Einstein condensates, or BECs, occur when gases are cooled to almost absolute 0. At these temperatures, quantum effects that are typically microscopic can become macroscopic. Jeff Steinhauer has done experiments with super-cold rubidium gas in a BEC state. Using a laser, it’s possible to effectively create a flow within the gas. When the laser pushes on the gas, the rubidium atoms want to move out of the way of the beam. Here, the edge of the laser acts as the event horizon—the rubidium atoms don’t have enough energy to jump back up over the waterfall. 

Still, as with real black holes, some atoms do escape as Hawking radiation. Here you can measure not just the existence, but also the temperature of the Hawking radiation. Taking the temperature of the evaporating particles from a BEC provides the strongest direct experimental evidence for Hawking radiation of a black hole. 

Besides rubidium gas, there are other quantum systems which physicists are using as analogs. Some are even quantum optical analogs, in which light sees an apparent horizon—usually caused by some clever material that’s used to slow the light down. But even these quantum optical analogs are at best, approximations of the dynamics at play with black holes.

In some ways, the crux of the matter is as much philosophy as physics: How much can analog black holes actually tell us about real black holes? Early arguments in the late ‘90s claimed that because Hawking radiation should appear for a variety of systems—you just need some sort of apparent horizon then finding bonafide Hawking radiation for one system should tell you about Hawking radiation in black holes. True Hawking radiation need not necessarily depend on a specific theory of quantum gravity. Proponents of this line of thought have triumphantly pointed to experimental observations of analog Hawking radiation—in laser pulses, fluids, and BECs—as proof-positive of Hawking radiation in black holes. 

Others acknowledge the experimental evidence of analog Hawking radiation in these other systems means something, and may be complementary evidence that has some significance for black holes—but insist that analogs are not a true proxy. And some remain quite skeptical, claiming that analog Hawking radiation doesn’t even meet the standard of complementary evidence. Black holes are unique aberrations, and analog is just that: an imperfect analogy incapable of truly capturing the extreme dynamics at play.  

But until we’re able to travel to the stars, or to build - and hopefully control - real black holes in the lab, the black hole analog is the best physical experiment we can do. The black hole theorists will continue to theorize, but now we have a new daring breed of black hole experimentalist - and the secrets they pull from the bathtub vortex may give us the next great insight into black holes, Hawking radiation, and the nature of spacetime.