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So say there is an object that is in the form of gas and dust and a core that weighs 10 earths is in the center and there is a sphere of gas around it that weighs 50 Earths, so the final mass is only 60 Earths and say after collapsing the radius is 5 Earth radii.

So technically the object doesn't collapse into a black hole but wouldn't the fact that when it is collapsing the object is technically getting closer and closer to its Schwarzschild Radius technically produce Hawking radiation because there is an apparent horizon even if the actual event horizon will not form due to the materials and masses involved. The metric doesn't care about whether the object will collapse into a black hole at the end, but whether it looks like it will collapse into a black hole. So any minor collapse would still cause an apparent horizon right?

But where would the energy for the Hawking radiation then come from, because technically speaking the object is still outside the Schwarzschild radius so it can't come from the mass within the object outside of just the gravitational potential energy right?

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    – Buzz ♦
    Commented Mar 6 at 1:33

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But where would the energy for the Hawking radiation then come from, because technically speaking the object is still outside the Schwarzschild radius so it can't come from the mass within the object outside of just the gravitational potential energy right?

This is already a great argument for why there will be no Hawking radiation. However, it doesn't quite answer the interesting bits, so let me complete the answer.

Hawking radiation is not a prediction of general relativity, but rather of quantum field theory in curved spacetime. This is relevant because this means the physics involves two complementary ideas:

  • quantum observables, which are local objects built out of the quantum fields;
  • states, which are highly non-local objects that depend on the entire structure of the spacetime.

Hawking radiation is a prediction concerning a specific state on Schwarzschild spacetime: the Unruh vacuum. What is important about this is that the Unruh vacuum is not defined locally (it doesn't even make sense to talk about a state locally), but rather globally. The Unruh vacuum knows that there is an event horizon and part of the reason we get Hawking radiation is precisely the behavior of the Unruh vacuum near the event horizon. By modifying this behavior, we can get to a completely different state, such as the Boulware vacuum, which is a physical state for a compact object with no event horizon. The mere presence of an event horizon can change deeply the aspects of the quantum state of the fields on your spacetime and hence change aspects of particle production.

Locally, you are correct. The metric in a local region of spacetime does not care about the existence of an event horizon. However, gravitation is not only about local constructions: there are very relevant physical consequences of nonlocal aspects of the spacetime. Hawking radiation is one of them.

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  • $\begingroup$ So does the Hawking Radiation have a delay because technically when an event horizon forms, the space-time around it only knows about it at the speed of light, so then only after that information reaches it does the Hawking Radiation start right because hawking radiation happens in space around horizon so once the information goes to a little bit bigger than the actual size of the black hole to where the Hawking Radiation can originate from? $\endgroup$
    – Roghan Arun
    Commented Mar 6 at 3:23
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    $\begingroup$ @MiltonTheMeme As observed from outside, the event horizon never forms in the eternity of the cosmological time. $\endgroup$
    – safesphere
    Commented Mar 6 at 6:05
  • $\begingroup$ @MiltonTheMeme As safesphere correctly pointed out, the event horizon never forms in the perspective of an outside observer. The physics of Hawking radiation is more subtle, because it is highly non-local. Correlations in quantum fields are not restricted to the speed of light (as one can see by noticing the Feynman propagator does not vanish at spacelike events), so it is not a matter of the event horizon forming and then Hawking radiation occurring. Hawking radiation occurs at infinity even though an external observer never saw the event horizon form, and it happens due to the event horizon $\endgroup$
    – Níckolas Alves
    Commented Mar 6 at 11:28
  • $\begingroup$ This does seem a lot awkward, but again: the main point to take home here is that this is a highly nonlocal effect. It is incorrect to think of this effect as particles propagating on a spacetime, or being created near the horizon. The physics is much more complicated and highly nonlocal $\endgroup$
    – Níckolas Alves
    Commented Mar 6 at 11:29
  • $\begingroup$ So technically speaking there is a small amount of Hawking Radiation on Earth as well due to Sagitarius A black hole and technically speaking there is still some non zero radiation even over many millions of event horizon radii away?So it is not like something that happens within 10-20 event horizon radii. $\endgroup$
    – Roghan Arun
    Commented Mar 6 at 13:37

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