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Does a virtual particle that enters a black hole also become a real particle just like the one that escaped? If so then the mass taken away from the black hole by the escaping virtual particle would be replaced by the one falling into the black hole so the black hole doesn’t actually lose mass and evaporate away.

Qmechanic
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Christine Annette LaBeach
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  • Related: https://physics.stackexchange.com/q/132179/123208 & https://physics.stackexchange.com/q/251385/123208 Also see https://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html – PM 2Ring Dec 31 '20 at 09:55

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There are limits to how good the "virtual pair production" picture of Hawking radiation is. the only critical thing for making the Hawking radiation work is realizing that the vacuum state at infinity is different from vacuum state at the horizon, and because they are different, the horizon looks like blackbody radiation to someone at infinity. There are a large number of ways that that mathematical result can be turned into an intuitive result, but I wouldn't take any of them too literally.

Zo the Relativist
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  • This doesn't answer the question and is not helpful. What is the point of writing answers accessible only to specialists who already know the answer? – safesphere Dec 31 '20 at 05:14
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    @safesphere: I strongly think that a lot of the talk about "virtual particles" is actively distracting to people, becasue they can lead to wrong conclusions from non-technical people, and "virtual particles" are perhaps the most technical construct in common use, being abstractions that exist only as subcomponents of fenyman diagrams, which themselves, are only a way to summarize a perturbation theory. – Zo the Relativist Dec 31 '20 at 14:32
  • Agreed, but your answer could explain this point a lot better and in the language accessible to non-specialists. As it is, your answer assumes that the reader already knows what you are talking about and therefore provides no value. Readers who understand what you are saying already know your point while everyone else has no clue what you are talking about. – safesphere Dec 31 '20 at 16:15
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Does a virtual particle that enters a black hole also become a real particle just like the one that escaped?

Yes. Within this “pair production” picture, this second part of the pair, a particle that falls into the black hole is also real.

If so then the mass taken away from the black hole by the escaping virtual particle would be replaced by the one falling into the black hole so the black hole doesn’t actually lose mass and evaporate away.

That is wrong, because this second real particle has a negative energy (relative to a static asymptotic observer). The energy taken away from the black hole by escaping particle equals up to a sign the energy carried by the second part of the pair. So “absorption” of such negative energy particles is precisely the mechanism for the mass loss of black hole.

Note, that for static (or almost static, such as slowly evaporating non-rotating black hole) spacetimes, particles can have negative energy only inside the black hole horizon, while to escape away from the black hole the first member of the pair must be strictly outside. We thus have a “barrier” separating possible trajectories that must be crossed via quantum tunneling. On the other hand for a rotating black hole there are negative energy trajectories even outside the horizon, within ergosphere. So it is possible to extract rotating energy from a black hole via purely classical processes such as Penrose process.

A.V.S.
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  • Since the in-falling particle inside the horizon has negative energy, wouldn't it be gravitationally repulsed from the singularity, yet still confined within the horizon? I get that its just an intuitive picture, but over time it seems like the horizon would shink from the outside but grow on the inside...It gets bigger on the inside!!(Dr. Who reference!) – R. Rankin Dec 31 '20 at 09:21
  • Inside the horizon singularity is the unavoidable future, no matter what the energy (positive or negative). And negative energy of the half of Hawking pair has the effect of decreasing the BH mass thus reducing its gravitational pull on everything outside. – A.V.S. Dec 31 '20 at 10:56
  • @R.Rankin: For an interesting take on “shrink from the outside but grow on the inside” have a look at this paper. – A.V.S. Dec 31 '20 at 11:00
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The black hole has to give energy to create two real particles (by some yet unknown mechanism), and it only gets one of the particles back, the other one escapes, making the black hole lose energy and eventually evaporating.

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    But I thought virtual particles are produced by the vacuum. – Christine Annette LaBeach Dec 31 '20 at 00:44
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    yes, but they become real when they get the energy to make them non-virtual –  Dec 31 '20 at 04:22
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    @Wolphramjonny the point is that there is a difference between the definition of "real" and "virtual" depending on whether you're looking from infinity or at the horizon, so some "virtual" particles near the horizon are "real" at infinity, and can be observed as blackbody radiation. The reason for this is that the definition of the quantum vaccuum state depends on the time coordinate, which is different in these two places. – Zo the Relativist Dec 31 '20 at 04:40
  • @JerrySchirmer what is exactly wrong in the single sentence that I wrote? –  Dec 31 '20 at 05:03
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    @WolphramJonny Having a physical intuition is a criminal offense on this site +1 – safesphere Dec 31 '20 at 05:23
  • @ChristineAnnetteLaBeach Virtual particles don't exist. Real particles are produced by energy: $-2,+1,=,-1$. Also, as we observe from outside, nothing ever enters a black hole. – safesphere Dec 31 '20 at 05:27
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    @Wolphramjonny: "By some unknown mechanism". There's nothing unknown, the ambiguity in the on-shell condition is the mechanism. – Zo the Relativist Dec 31 '20 at 14:29
  • @JerrySchirmer Don't we need to understand quantum gravity first? You should publish your ideas and get the Nobel prize –  Dec 31 '20 at 16:10
  • @JerrySchirmer The mechanism may be considered formally known for the quantum forces, albeit with a lot of mystery in its physical interpretation. For gravity however the same mechanism is only assumed with no experimental evidence whatsoever and a lot of theoretical contraversy. For example, the existence of the Hawking radiation depends on the frame in a direct contradiction to GR. I have a lot more faith in GR than in any unproven speculations. Therefore, the Hawking radiation does not exist until proven otherwise. And so its mechanism is not only unknown, but at this point non-existent. – safesphere Dec 31 '20 at 18:32
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    @Wolphramjonny: this is a semiclassical result that doesn't depend on quantum gravity. It's like saying that the standard derivation of the hydrogen spectrum is wrong because there's no QFT in the problem. – Zo the Relativist Dec 31 '20 at 22:11
  • And seriously, all of this depends on is the definition of "particle" from the normal/time ordering of QFT operators, which is more mysterious than the GR aspect of this. if the full quantum gravitational theory isn't perturbatively close in a way that semiclassical gravity is valid for the case of macroscopic black holes, then I personally have trouble seeing how a theory can asymptotically match the classical GR tests. – Zo the Relativist Dec 31 '20 at 22:14