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Does Hawking radiation assume that general relativity works perfectly, inside black holes, or on the event horizon?

Could someone please tell me the exact statements made in describing Hawking radiation? (Before we apply the math).

Would the concept of Hawking radiation be moot if general relativity somehow failed, inside a black hole, since at this point we only have a theoretical model for a black hole?

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    $\begingroup$ Possible duplicate of An explanation of Hawking Radiation $\endgroup$ Sep 20 '17 at 15:21
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    $\begingroup$ Yes. Hawking's calculation takes spacetime to be curved in the way described by GR, and it uses this fixed geometry to do the quantum field theory calculation. So it does assume GR holds. $\endgroup$ Sep 20 '17 at 16:12
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    $\begingroup$ The calculation Hawking himself did assumes that GR holds exactly everywhere. However it is really only the presence of a horizon that causes radiation to be observed. So even variants on GR like Brans-Dicke would still predict radiation as long as a horizon is present. GR would have to fail so badly that there was no event horizon for the Hawking radiation to fail to exist. $\endgroup$ Sep 20 '17 at 17:16
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    $\begingroup$ For close voters - I don't believe this is a duplicate, as it's asking for the assumptions behind hawking radiation, not a description of it. $\endgroup$ Sep 20 '17 at 20:29
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    $\begingroup$ We have no reason to doubt that GR works under the conditions that are present at the event horizon of a black hole. The conditions under which we expect GR to fail are those in which the curvature of spacetime was comparable to the inverse of the Planck scale. Those are conditions that apply near the singularity, not at the horizon. $\endgroup$
    – user4552
    Sep 20 '17 at 23:08
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First let me direct you to An explanation of Hawking Radiation where I have attempted an accurate but relatively accessible explanation of the mechanism for Hawking radiation.

To address your specific points: Hawking's original calculation assumed that general relativity gives the correct description of the spacetime every inside and outside the black hole event horizon. He used quantum field theory in the curved spacetime predicted by GR to perform his calculations.

However the key feature that causes the radiation is the presence of a horizon, so alternatives to general relativity like Brans-Dicke theory also predict Hawking radiation as long as a horizon is present. General relativity would have to fail so badly that no event horizon exists for there to be no Hawking radiation.

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No, we do not need to assume general relativity in order to predict Hawking radiation. In fact, the opposite is true. Hawking radiation is a prediction of semiclassical gravity, which is a method in which assumptions are made that violate general relativity. (And there is no other choice, since general relativity and quantum mechanics are incompatible.)

Actually, Unruh radiation is predicted to be emitted from any horizon. This includes event horizons in flat spacetime, which has no gravitational fields at all. Such a spacetime can be described using pure special relativity, with no need for general relativity.

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  • $\begingroup$ The other choice that you may have overlooked is ECT, as described in my answer & its link. Also, the cosmology tag would seem to create a problem with any total lack of a gravitational field, regardless of whether its effects would be dependent upon spacetime curvature or upon hypothetical gravitons. $\endgroup$
    – Edouard
    Jan 25 at 2:47
  • $\begingroup$ For anyone just tuning in, I have to point out the fact that the cosmology tag preceded user286880's answer by only 11 min., so it may've been formulated without his taking it into account. $\endgroup$
    – Edouard
    Jan 25 at 2:59
  • $\begingroup$ The currently-unchallenged Wiki "Unruh effect" points out the fact that no detection of that effect has been generally accepted: I believe that the same is true of Hawking radiation, although its origin in or extremely close to causally-separated regions (black holes) might leave the failure to detect it within the few decades since it was hypothesized seem a little more consistent. $\endgroup$
    – Edouard
    Jan 25 at 5:43
  • $\begingroup$ "His" in my 2nd comment was a typo for "their", the generic article for individuals and groups. $\endgroup$
    – Edouard
    Jan 25 at 18:01
  • $\begingroup$ Even if it does occur, there are problems with the Unruh effect in a cosmological context, as per Anders Sandberg's recent answer to the PSE question at physics.stackexchange.com/questions/608821/… . $\endgroup$
    – Edouard
    Jan 25 at 19:01
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Hawking radiation, which has not been observed, has been hypothesized as a resolution of the Black Hole Information Loss Paradox, whose resolution is necessary for that preservation of unitarity which is central to the current formalism of quantum mechanics.

Since the 2017 answer, a 2019 paper has appeared at https://arxiv.org/abs/1910.10819 , which makes a good case for resolution of the Black Hole Information Loss Paradox by passage of the information, within black holes formed by stellar collapse, to another local universe (possibly like our own, but presumably much smaller) "parented" within it, which will eventually contain black holes of its own, in a process that may continue ad infinitum. This passage of information, actually sketched in simpler terms by John Preskill at https://arxiv.org/abs/hep-th/9209058 in 1992, might preserve the unitarity of quantum physics without the extremely faint radiation conjectured by Hawking, which, at least without phenomenal magnification energy or one very long wait for some stellar collapses much closer to us than those already observed, is extremely likely to remain entirely hypothetical.

The "parenting" process involved may use GR in the formation of the black holes, but uses 1929's Einstein-Cartan Theory within them.

ECT, worked out thru conversations between Einstein and the great mathematician Elie Cartan, differs from GR in positing some TINY spatial extent for fermions (subatomic matter particles), which is essential for the torsion-based bounce effects involved in the formation of the LU's. After the discovery of particulate spin in the mid-1920's, the idealization of fermions as being absolutely point-like derived from Pauli, who realized that their rotation rate might otherwise exceed the speed of light. Although the reductions in that speed that occur when light rays enter material as common as water were known at the time, the possibility of smaller local universes whose average density might be much greater than our water's did not occur to Pauli, and Cartan laid it by that wayside where so many of physics' past "absolutes" remain. (Einstein had no objection to that, as his 1916 pop-sci book on 1915's GR mentioned just such "local" possibilities, but they hadn't been written into the formal theory, which antedated "multiverses" by several decades, and required observational or experimental proof.)

The 2019 paper I've linked to my answer requires, for its own observational proof, universal rotation, a concept often misunderstood because it may involve numerous axes. Astronomical results that might substantiate it have varied.

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  • $\begingroup$ To see further discussions of past- and future-eternal "black hole genesis" cosmologies, as well as possibilities for observational proofs of them in Skydivephil's interviews with Smolin, Poplawski, and other major physicists, go to youtube.com/watch?v=xXL0N3elFLE . $\endgroup$
    – Edouard
    Jan 26 at 14:34

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