Let us continue our exploration of the physics of black holes and especially of the physical phenomena that take place very close to the horizon of black holes. Now here is a black hole with its central singularity and which is protected by the horizon. And outside of the black hole we have the vacuum. We have seen that the vacuum is the location of fluctuations– quantum fluctuations. And so, for example, in this place, here, we have the production of an electron and an antielectron, which annihilate. And we have seen that this phenomenon occurs if the violation of energy conservation lasts a very microscopic duration of time. And so that happens everywhere in the vacuum outside the horizon.
But it also happens just outside the horizon. So let me, again, consider fluctuations, but very close to the horizon. So we have the formation of a pair of an electron and the antielectron. And just imagine that we are so close to the horizon that the antielectron is crossing the horizon. Then it’s lost forever. And eventually it will get to the singularity of the black hole. Now the poor electron has nobody to recombine with. And so it will continue all the way to infinity and taking away an energy E = mc2.
And so you see that this quantum process, which corresponds to fluctuations very close to the horizon, leads to a particle taking away an energy mc2 Well, where does it take it from? Well, it takes it from the mass energy of the black hole. And so that means that, in this process, which is called the “Hawking radiation”– this is a radiation going away– the black hole is losing an energy mc2. And so its mass is slightly diminishing. And so, little by little– because you have fluctuations everywhere– little by little, the black hole will lose some mass through Hawking radiation. It will, we say, “evaporate.”
And so, because of this phenomenon, black holes will evaporate, will lose energy, and eventually they will have a finite lifetime. They will disappear.
There are heated debates among theorists about the way information is treated at the level of the horizon of a black hole. So let me illustrate this with a very simple example. I’m standing here, exactly at the horizon. I have one foot on one side, on the exterior, the other foot on the inside, on the side of the singularity of black hole. And now, see what happened?
On the outside, I have a blue sock. On the inside, I have a red sock. Now you understand that, of course, this information of a red sock cannot get outside, because that would mean that some information is getting out of the horizon of the black hole. On the other hand, I can send the information that I have a blue sock on the outside– I can send it inside of the black hole. And so that means I could send only from this side to this other side any information. So you see what happened? This morning, I had two blue socks. I put this foot inside the horizon of the black hole.
It changed the sock without telling me, because it is becoming independent. And from now on I have no way of knowing– because I have no way of extracting information from the side of the black hole where there is a singularity.
Let us think in more details which information went into the black hole. This morning, when I woke up, I put two blue socks on. And so the information that went into the black hole is the information of a blue sock. And so you see that, in a sense, it is as if this information was lying on the surface of the horizon. And indeed, one has a picture similar to this one, here, of the horizon of a black hole being a sphere which is papered with information which carries all the information that went into the black hole. Because all that information had to cross the horizon.
So sometimes one gives the idea of an hologram– you know, the hologram is a two dimensional surface that carries all the information of a three-dimensional picture. Well, in a sense, the horizon can be thought of as an hologram. Now there is a difficulty associated with the phenomenon of Hawking radiation that we just discussed.
Let me imagine that I crossed the horizon with my two blue socks. In principle, that information is lost to the world. Now we wait long enough so that the black hole evaporates completely, because of the Hawking radiation. Now the question is– and this is a question of great debate among theorists– the question is the following. The information of my two blue socks, which was lost to the world– is it going back into this world, once the black hole has completely evaporated? In other words, is this information lost forever, or is this information recovered once the black hole has completely evaporated?
To summarise, we have seen that the horizon is the surface of no return. But if we stay outside the horizon of a black hole, then we can orbit around the black hole. The black holes of general relativity are rather simple objects. We have seen that their properties are characterised by three numbers– their mass, their charge, and their angular momentum. The horizon is the location of remarkable phenomena, in particular the Hawking radiation. We have seen that this phenomenon allows black holes to lose progressively energy and is responsible of their ultimate evaporation.