2.2 Hawking Radiation and Information Loss

summary

Quantum fluctuations can spontaneously create short-lived particle pairs.

According to quantum mechanics a vacuum is not really empty but is teeming with fluctuations.
These energy fluctuations spontaneously create particle-antiparticle pairs, like electron-positron pairs, that almost immediately annihilate each other.
Each particle requires energy ($E = mc^2$) that is “borrowed” from the vacuum.
The lifespan of these pairs is limited by the uncertainty principle, so that the more energy borrowed the shorter the lifespan before the two particles annihilate: $$\Delta E \Delta t \simeq \hbar$$

The situation changes near the event horizon of a black hole.

A vacuum fluctuation that occurs very near to the event horizon does not have to annihilate.
We saw that a particle inside the event horizon has net negative energy, while a particle outside has net positive energy. If a vacuum fluctuation occurs very near the event horizon, one particle can fall in and the other fly away; their net energy will balance to 0.
Since the net energy ($ΔE$) is 0, the lifespan of the particles ($Δt$) can approach infinity and they still never have to recombine. The emitted particle is called Hawking radiation.
Over the course of many Hawking processes the black hole is going to have less and less mass as more negative energy particles fall into it, eventually turning the black hole into a massless remnant.

Hawking radiation carries no information about the black hole that emitted it.

Two black holes, each formed from a different type of star, both emit radiation that carries no information about their initial states.
All the information about the objects the black holes evolved from is trapped behind the event horizon. The emitted Hawking radiation comes from the vacuum, which is the same everywhere, so it carries no information about its source black hole.
Energy has been recovered in the form of the Hawking radiation, but information about the objects that became black holes is irreversibly lost.

Nowhere else in physics is information permanently lost.

In both classical and quantum physics, changes of the universal state can be tracked and reversed, even if performing those reversals is practically impossible. Information can be distorted from one form to another, but it is never lost. This is another way of saying that the laws of physics are deterministic.
Black hole formation and evaporation violate quantum mechanics because in quantum mechanics we can always turn back processes and infer the initial state. Hawking radiation, however, cannot tell us anything about a black hole’s unique initial state.
Surface features of other astronomical objects, like stars, create unique radiation patterns that allow observers to measure details about the sources.
We cannot attribute any such surface features to black holes as we currently understand them, because any unique structure lying on the event horizon will simply fall in. John Wheeler summarized this with the phrase “black holes have no hair”.