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On the horizon of a black hole negative energy (frequency) states of virtual particles are separated from positive energy states, while staying entangled. The negative energy states (particles or anti-particles) disappear behind the horizon, while the positive energy states take off for the wide space.

To carry away the information of the particles in the hole though, the outgoing state has to "know" the inside information. How is this information imparted to the outgoing radiation? Were the infalling particles that constitute the hole entangled with the vacuum in the horizon when falling through it? Is maybe the infalling negative energy state entangled with the inside particles, thereby teleporting the inside state to the outgoing particle, which thereby gets disentangled?

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    $\begingroup$ this understanding of Hawking radiation is incorrect, see e.g. this answer by John Rennie explaining that Hawking himself cautioned against using the idea of virtual particles as anything other than a heuristic. $\endgroup$
    – ACuriousMind ♦
    Jan 13 at 15:45
  • $\begingroup$ @ACuriousMind But can't the situation be described with the math of virtual particles, without considering them real? Don't negative frequency states move inside? Aren't they excited by creation operators? $\endgroup$
    – Deschele Schilder
    Jan 13 at 15:53
  • $\begingroup$ @ACuriousMind In his answer he says to commit the sin of taking quantum fields as resl objects. Why is that a sin? Are particles the real stuff? $\endgroup$
    – Deschele Schilder
    Jan 13 at 15:55
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    $\begingroup$ see this answer of mine for more discussion on the nature of virtual particles, I don't know what "negative frequency states" or "the math of virtual particles" is supposed to be, exactly. $\endgroup$
    – ACuriousMind ♦
    Jan 13 at 16:02
  • $\begingroup$ @ACuriousMind Isn't the mathematical language of virtual particles used in interactions? Can't this language be used here? The geometry of the vacuum exciting real particles from the virtual states as mathematical objects? Anyhow, how is the information of the inside particles transferred to the Hawking radiation, heuristically? $\endgroup$
    – Deschele Schilder
    Jan 13 at 16:10

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As mentioned in the answers linked in the comments to the post (see, for example, the answers to An explanation of Hawking Radiation), the notion of particle does not make sense in curved spacetime (or even in flat spacetime, if you consider non-inertial observers). If you're interested in a more mathematical explanation (i.e., if you have studied QFT before), this post has an outline of the derivation without actually opening up all of the calculations.

As for the entanglement issue, notice that the gravitational field doesn't really play a role in your question. As an example, consider the following situation. someone picks a coin and cuts it in half, separating heads from tails. This person then puts each half in a closed box and gives one of the boxes to me and the other to you. They then instruct me to go to Alpha Centauri (4 light-years from here) and only then open the box.

The second I open the box, I see I have the heads side. Hence, I immediately know you have tails, even though you are four light-years away. How could I know that so fast without violating causality?

The point is that causality was never violated. There is a correlation between the sides of the coin that exists since well before I traveled to Alpha Centauri. Similarly, in Hawking radiation, there are quantum correlations in the quantum fields. Or, pictorially, between the "particles". The field outside doesn't have to know what is going on inside because the information that fell in was correlated to the information outside before falling in.

This is pretty much the meaning of entanglement. One can say that the modes that fell inside the black hole are entangled with modes outside of the black hole.

However, there is a caveat. If you only look at the information outside of the black hole, you cannot reconstruct the entire state. In other words, if you only have access to the outside of the black hole, you cannot know what is going on inside it, despite the correlations. For example, if I measure some property of a particle far away from the black hole (where the notion of particle actually has meaning), I will not be sure whether this particle is entangled to something inside the black hole or if it is not. This is why people talk about information loss upon black hole evaporation. The information that was inside the black hole simply vanishes, according to Hawking's calculation. Some physicists dispute the result, others agree with it. It is still a matter of debate whether this is actually an issue or not. If this interests you, I have discussed more about information loss in this post.

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  • $\begingroup$ Thanks for your answer. If one stays just above the horizon, will the radiation still be seen? Will an accelerated person in flat spacetime perceive a different vacuüm, or is it the inertial observer observing him/her? And how is the Hawking radiation entangled with the mater inside the hole? I mean, particles dó form te hole, don't they? $\endgroup$
    – Deschele Schilder
    Jan 15 at 10:16
  • $\begingroup$ @Cecil if you are hovering at a fixed distance, you see the radiation. If you're falling, you don't. The notion of particle depends on the observer. All observers in flat spacetime experience the same quantum state, but interpret it differently. An accelerating observer perceives it as a thermal state while an inertial observer perceives it as having no particles at all. $\endgroup$
    – Níckolas Alves
    Jan 15 at 14:18
  • $\begingroup$ Particles are an interpretation, so no, black holes are not made of particles, nor are we, in a fundamental sense. The fundamental constituents of the universe are fields. Particles are just a convenient way of thinking about fields. In flat spacetime, both points of view can be taken as nearly equivalent, but in curved spacetime or when one considers non-inertial observers the notion of particle becomes observer-dependent, and hence inadequate at a fundamental level $\endgroup$
    – Níckolas Alves
    Jan 15 at 14:23
  • $\begingroup$ Hawking radiation does not need to be entangled to the matter that forms the black hole, by which I mean the matter composing the star that collapsed to a black hole. An interesting feature of Hawking radiation is that it does not depend on the details of the collapse. Hence, the only entanglement relevant for the radiation itself is the one between modes of the field that I discussed. It might happen that the star was entangled to something else before the collapse, but the details of the star can't affect the radiation $\endgroup$
    – Níckolas Alves
    Jan 15 at 14:26

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