What is a Black Hole Laser?

When you grow up as a child that does not have to worry about being fed and housed and all that, you get to think about all kinds of awesome and fantastic things: Dinosaurs! Space ships! Black holes! Lasers!

What if you could combine all of those? Would that create the ultimate awe-pocalypse? Dinosaurs flying into black holes in spaceships powered by lasers? Obviously we can't pull this off because dinosaurs are extinct, we have a hard time building spaceships (though Elon is working hard to change that) and we certainly can't fly into black holes, even though movies such as Interstellar  have teased that. But where do Lasers fit in? Well, hold on to your seats: it appears that (at least theoretically) black holes can be turned into Lasers, or maybe some already are, but we don't know it yet! 

If you are reading this post you probably already know what Lasers are, but in order to make the case for BHLs (black hole lasers), let me reintroduce you to them briefly. `Laser' is an acronym for "Light Amplification by Stimulated Emission of Radiation" (be honest, it's one of the greatest Science Acronyms of all time, because it is not tortured at all). The phenomenon relies entirely on Einstein's work concerning the probability of absorption and emission of light from atoms or molecules. Here's the title of this groundbreaking (and, as a matter of fact, easy to read) paper:

In this paper, Einstein showed how you can derive Planck's celebrated formula (the "Law of Radiation", or "Strahlungsgesetz") from first principles. Yeah, Planck had essentially guessed his law. 

Einstein made the following assumptions, given an atom or molecule that has discrete energy levels with energies \(E_1\) (the "ground state") and \(E_2\) (the "excited state"):

1. A quantum of light can be absorbed by the atom, which raises the state from ground state to excited state 

Here, \(\hbar \nu\) is the energy of the quantum that is tuned to the difference in energies: \(\hbar\nu=E_2-E_1\).

2. If an atom is in its excited state, it can spontaneously emit a quantum of energy:

3. If an atom is in the excited state and absorbs a quantum at the same time, the quantum stimulates the emission of another quantum just like it:

Using these assumptions, Einstein was able to derive Planck's law, which in turn means that these are the only processes needed to understand how radiation interacts with matter (barring quantum field-theoretic effects, of course). 

The third process, called stimulated emission, is the one that gave us Lasers. The thinking behind is (in hindsight) quite simple. Take a look at the picture above. What happened here is that the incoming quantum was doubled (copied). You don't violate the no-cloning theorem this way because the spontaneous emission process provides just about enough noise. But you already knew this. Now suppose that after you made two-out-of-one, the two quanta go on their merry way but encounter a mirror and head back:

At the same time, imagine you have a way to "pump" atoms back to their excited state from the ground state (that's what the yellow light bulb in the sketch above is supposed to do). When the two quanta encounter an atom (not necessarily the same one, there will be plenty of atoms in the gas that's enclosed in the cavity between the two mirrors), each will stimulate the emission of a clone, so from 2 make 4. Because this doubling gives rise to an exponential process, after a short while the number of quanta becomes astronomical. Now, if the quanta remain in the cavity then they would be of no use to anyone, which is why one of the mirrors is usually made semi-transparent: so that the beam of coherent quanta can leave out of that side. That's your Laser, right there:

Alright, now that you have become a Laser expert, what does this have to do with black holes? Those of you that have been following this blog from its inception maybe remember that stimulated emission is precisely the process that saves information from disappearing into a black hole (if you haven't, then start here). In a nutshell, the processes that Einstein wrote about don't just hold for light interacting with atoms, they hold for any and all particles (fermions or bosons) interacting with any matter. In particular, they hold in quantum field theory. And as a consequence, they hold for quantum field theory in curved space. They hold for stuff interacting with a black hole. So when a particle is absorbed by a black hole, it stimulates the emission of a clone outside the horizon (which is carrying a copy of the information), and so we don't have to worry about the one that disappears behind the horizon. That's it, that's the whole ballgame for solving the problem of information loss in black holes. If you take into account this process (instead of ignoring it, as Hawking did in his calculation [1]) you find that information is conserved (the capacity of the black hole to process classical information is positive). 

"Fine (I hear you saying), but this doesn't make a Laser yet"!

True. For example, where's the mirror? But, hear me out. Suppose you fell into a black hole (one that is very large, so you don't get ripped apart by the tidal forces), and suppose you brought with you some rocket engines that would allow you to hover inside the event horizon, but you don't fall towards the singularity (if there is one). Even better, imagine that there are planets inside the black hole (like in the movie Interstellar, again). Then you would "look up" to the horizon, and you would notice something strange. If you shine a light beam towards the horizon, it is reflected back. The reason for this is simple: nothing can escape the black hole, so the best that your light beam can do is "go into orbit" below the event horizon. Basically, this means that from inside of a black hole, you're looking at a white hole horizon. (I've written about this before: it is a consequence of time-reversal invariance.)

The other thing you have to keep in mind when discussing stimulated emission in quantum field theory is that you always "stimulate in pairs". The reason for this is that you need to conserve quantum numbers: for example, if you are going to stimulate an electron, you are going to have to stimulate a positron also. So for every clone that is stimulated outside of the horizon, you also stimulate an anti-clone inside of the black hole (see Fig. 1)

Fig. 1 The horizon of a perfectly absorbing black hole looks black from the outside, and white from the inside. Particle p (black) is absorbed, and stimulates the emission of the clone-anticlone pair (red).

But clearly that is not enough yet to make a Laser. So imagine then two black holes that are connected by an Einstein-Rosen bridge: a wormhole. This might look a bit like this:

Wikipedia's depiction of a Schwarzschild wormhole. 

Basically, it is two black holes connected by a "throat". We don't know if it's traversable for people, but you certainly can imagine that a particle thrown into one of the black holes might come out at the other end. 

Come out? But nothing can come out of a perfectly absorbing black hole, right? Well, this is both right and wrong. Physical particles cannot come out, but you can clone those particles, so copies can come out, which after all is just as good. 

Let's see how this would look like. We now take the black hole horizon from Fig. 1, and add another one like so:

Fig. 2: Two connected black holes with horizons \(H_1\) and \(H_2\). The anti-clone that travels towards \(H_2\) is reflected there, and stimulates another pair.

Because from the inside the black hole looks like a perfectly reflecting white hole, the anti-clone heads back to horizon \(H_1\), but the mathematics of stimulated emission in black holes says that the reflection creates a clone pair as well. 

What happens now? Well it's clear. The absorbed particle and one of the anti-clones are on a collision course leading to annihilation, but the other anti-clone will reflect on \(H_1\) and stimulate another pair. As if by magic, there are now two clones outside horizon \(H_1\), and two outside horizon \(H_2\). But the anti-clones inside the wormhole keep reflecting between the horizons just as in the optical Laser described above. Except that we don't need semi-transparent mirrors: the "Laser beams" will emanate from the horizon in a coherent manner as long as the inside of the wormhole is coherent!

Fig. 3: The wormhole Laser. Anti-clones that are reflected from the inside of the black holes stimulate emission of clones outside the respective horizons. 

So where does all this energy come from? After all, there is no pump that "charges up" this Laser, as there must be for an optical Laser. The answer is that this bill is paid for by the black hole's masses, just as it is in spontaneous emission. A detailed calculation would have to show how fast a wormhole might deplete its mass, but the calculation is already difficult for a single black hole (and it can only be made by approximating the interaction between black hole and radiation with a model, see here). 

Now to the last question: what would a BHL look like? First of all, it is clear that whatever radiation emanates from the black hole, it will look like it is coming from a disk surrounding the black hole. We also know from explicit calculations that the stimulated emission in response to absorbed material is not red-shifted (because this is "late-time" absorption). However, what happens to material that reaches the second horizon I can't say without a calculation. The important distinction for Laser light, however, is that it is coherent. If the stuff that is stimulated outside the horizon is similarly coherent, we might be able to detect this using typical Hong-Ou-Mandel interferometry of light coming from such a black hole. We've just learned how to look at light emitted from black holes using telescopes like the Event Horizon Telescope, so it might be some time before we can check if that light is really BHL light. We don't know how many black holes are actually connected to others making BHLs possible, but at least there is a chance to find out! 

[1] The reason Hawing ignored stimulated emission in his calculation of radiation coming from a black hole is that he thought that it would require energy from a black hole's rotation (the rotational energy would provide the "pump energy"). Because he treated a non-rotating black hole, he decided he could ignore the effect. It turns out that stimulated emission does not require black hole rotation.