Radiation pressure from Hawking radiation, or "Do black holes ever actually form?"

[Linguofreak]

Radiation pressure from Hawking radiation, or "Do black holes ever actually form?"

When reading scientific literature on black holes, one generally hears the collapse process and the release of Hawking radiation discussed separately, though this article:

http://xxx.lanl.gov/abs/gr-qc/0304042

seems to indicate that Hawking radiation is actually driven by the collapse process itself, and that an object that does not collapse completely will radiate until it reaches its final radius (as seen by outside observers). But even the above article doesn't discuss the interaction of Hawking radiation and infalling matter beyond its relation to the production of Hawking radiation in the first place.

Near the horizon, without much gravitational redshift, or in the case of small black holes, Hawking radiation is extremely intense, according to one calculator I found, a 100 million metric ton hole would radiate 25 gigawatts from a surface area of 0.4 square femtometers, which is about a tenth the mass of Earth (times c^2) crossing every square meter of horizon area every second (of course, it has nowhere near a square meter of horizon area).

So can the radiation pressure from Hawking radiation prevent infalling matter from crossing the event horizon? Even if not, a black hole has a finite mass, and it seems to me that an infalling observer is likely to see that mass of Hawking radiation pass by them before they cross the horizon (in other words, they'll observe the hole to radiate itself away to nothing below them).

So would a black hole ever actually form? That is to say, would the interior part of the Schwarzschild geometry ever actually form, or would we just get an object that looks asymptotically like a black hole from the outside (collapsing to a radius asymptotically close to the Schwarzschild radius for the mass involved and radiating itself away in approximately the right timeframe), but with no actual event horizon or singularity?

 

[jedidia]

That was... surprisingly understandable, and rather fascinating. Since within the event horizon time passes extremely slowly, it might indeed be very well possible that what we perceive as a pretty stable phenomenon from the outside is something aproaching a violent explosion within. Physics is weird...

 

[Linguofreak]

That was... surprisingly understandable, and rather fascinating. Since within the event horizon time passes extremely slowly, it might indeed be very well possible that what we perceive as a pretty stable phenomenon from the outside is something aproaching a violent explosion within. Physics is weird...

Time flows slowly near the horizon (assuming it actually forms), not within it, actually. The gravitational time dialation factor between a point external to the black hole and a point within the horizon is actually an imaginary number (which is to say, time and the radial coordinate switch places when you cross the horizon). The fact that Hawking radiation increases in intensity without limit as you approach the horizon is well known enough (assuming that Hawking radiation does in fact happen, which is disputed by some), my question has more to do with the impact that that has on whether black holes actually form at all.

 

[jedidia]

Yes, I was mixing up my terminology.

Now black holes, as they go, seem to be a fairly well-proven phenomenon. The question here would be if the singularity that is supposed to be in their center actually forms, or if the whole thing (in its own reference frame) just blows up before it can come to that, at least as far as I understand it.

Of course it could be argued that this wouldn't really be a black hole anymore, but I think that's more semantics... It's still a better term than "Crazy gravity source from which light has a really tough time to escape".

 

[Fizyk]

But even the above article doesn't discuss the interaction of Hawking radiation and infalling matter beyond its relation to the production of Hawking radiation in the first place.

Near the horizon, without much gravitational redshift, or in the case of small black holes, Hawking radiation is extremely intense, according to one calculator I found, a 100 million metric ton hole would radiate 25 gigawatts from a surface area of 0.4 square femtometers, which is about a tenth the mass of Earth (times c^2) crossing every square meter of horizon area every second (of course, it has nowhere near a square meter of horizon area).

So can the radiation pressure from Hawking radiation prevent infalling matter from crossing the event horizon?

As far as I know, infalling matter probably wouldn't even experience any Hawking radiation.

There is a thing known as the Unruh effect: what is a vacuum for one observer doesn't have to be a vacuum for another one. For example, an accelerating observer will measure a thermal spectrum of particles in what is a vacuum to an inertial observer, and vice versa.

Unruh effect works in a flat spacetime, and black holes are in a curved spacetime, but the principle is the same. As far as I know (but I may be wrong here), Hawking radiation appears in that way: what is a vacuum to an inertial, infalling observer, will be a thermal spectrum of particles to a stationary (and therefore accelerating) observer. So what we would perceive as Hawking radiation emitted by the black hole would be actually a vacuum to the infalling matter.

 

[Linguofreak]

As far as I know, infalling matter probably wouldn't even experience any Hawking radiation.

There is a thing known as the Unruh effect: what is a vacuum for one observer doesn't have to be a vacuum for another one. For example, an accelerating observer will measure a thermal spectrum of particles in what is a vacuum to an inertial observer, and vice versa.

Unruh effect works in a flat spacetime, and black holes are in a curved spacetime, but the principle is the same. As far as I know (but I may be wrong here), Hawking radiation appears in that way: what is a vacuum to an inertial, infalling observer, will be a thermal spectrum of particles to a stationary (and therefore accelerating) observer. So what we would perceive as Hawking radiation emitted by the black hole would be actually a vacuum to the infalling matter.

I'm no expert on Hawking radiation myself, but the article I linked seems to indicate otherwise (stating that an infalling observer will observe trans-Planckian wavelengths about a Planck time before crossing the horizon).

Also, if no unaccelerated observer ever observes any kind of Unruh/Hawking radiation, wouldn't an observer orbiting a black hole also not see Hawking radiation?

From what I've read, it seems to be the presence of a horizon that is the key factor: For the Unruh effect, in the unaccelerated case there is no horizon, while in the accelerated case one observes an acceleration horizon from which the radiation seems to come (to abuse the terminology somewhat, as horizons are by definition unobservable and everything that is observable is on the near side of the horizon. But there is a surface that serves as an asymptote that observable things are seen to approach but never cross). For a black hole, an unaccelerated infalling observer still "sees" a horizon as long as the collapse continues, which is until the observer reaches the singularity in the traditional black hole case (and, per the above article, when the collapse stops, the radiation stops).

The above probably isn't the best formulation of what I'm trying to say (I'm not really sure it's proper to talk about a horizon in the Hawking case if the collapse doesn't continue through the Schwarzschild radius), but I hope it gets across how I understand things to work.

 

[Fizyk]

Well, looks like I'm going to have to read and understand that article

Also, if no unaccelerated observer ever observes any kind of Unruh/Hawking radiation, wouldn't an observer orbiting a black hole also not see Hawking radiation?

I have no idea. According to what I said before, apparently not, but 1) the nonzero curvature might change something, 2) it's possible that I understand this whole thing totally wrong. I need to read more on the topic.

 

[Capt_hensley]

My quandry has always been this...

Nothing travels faster than light,

Light cannot escape a black hole,

Radiation is nothing more than high energy particles, Light is nothing more than high energy particles, how can hawking radiation escape from a black hole?

 

[Urwumpe]

Radiation is nothing more than high energy particles, Light is nothing more than high energy particles, how can hawking radiation escape from a black hole?

Because it doesn't come from within the event horizon, but is produced a short distance outside. In any volume with non-zero field energy, pairs of particles and anti-particles are created spontaneously and extinguish each other after a short moment. Contrary to usual matter-antimatter reactions, no energy is emitted as photon when both particles collide again, since both particles had only been virtually existing for giving the volume its field energy (For logic geeks: Iff you have such particle pairs appearing out of nowhere, you have non-zero field energy).


This means that the energy balance is zero, conservation of energy still applies, the energy in the universe does not change.

When one of the particles of a pair drops into the black hole, the energy balance is no longer zero, because half of the energy is suddenly in the black hole. Since the energy sum of the particle pair is zero, regardless which particle of the pair is absorbed, the black hole has to lose energy by absorbing this particle, when the other particle escapes and keeps on existing in the universe.

If both particles would be absorbed - energy balance is again zero and nothing happens at all.

Understandable? I tried to steer clear of too much technobabble there.

 

[Capt_hensley]

Yeah, you did OK there.

If you split particle pairs, and one is lost into the black hole, the other is radiated away from the black hole. Hence Hawking Radiation?

 

[Urwumpe]

Yeah, you did OK there.

If you split particle pairs, and one is lost into the black hole, the other is radiated away from the black hole. Hence Hawking Radiation?

Essentially yes - in reality both particles don't actually exist, until the black hole absorbs one of the particles. There are some more details in the real theory, but there are pretty hard to understand and harder to explain without understanding them. :facepalm: