Photon pressure within a black hole

[bcrelling]

If a large mass of matter and anti-matter collided to form a black hole, I assume they would anihilate and you would have a black hole made of photons. Now considering the black hole as a container of photon, there must be a net pressure pushing against the confines of the gravity.
The force of gravity increases with the inverse square of the radius, however the photon pressure increases with the inverse cube, meaning at a certain distance from the singularity the photon pressure with overcome the gravity. Also as far as I can see from the maths, if a black hole shrinks through evaporation, there will come a point when the photon pressure will supersede the event horizon, and boom would the black hole simply explode?

 

[jedishrfu]

If antimatter fell into the black hole nothing special would happen other than the hole gets a little larger.

Once it's past the event horizon it's not coming out. So basically you won't see any photons even if it did collide with matter on the way in.

When anything falls into a black hole it follows a trajectory toward the singularity but never reaches it. It basically squished and stretched out as it falls. There is no matter at the center of the singularity.

http://en.m.wikipedia.org/wiki/Black_hole

With respect to your question, it seems if the black hole formed the photons would be trapped inside falling toward the singularity. They would lose their sense of being photons as only their properties of mass, charge, and angular momentum are preserved...

Black holes do evaporate and go out in a flash of light. I can't comment on the photon pressure though I couldn't find any reference for it.

 

[PeterDonis]

considering the black hole as a container of photon

It isn't. A black hole isn't a "container" of anything. Everything inside a black hole is falling into the singularity. See further comments below.

there must be a net pressure pushing against the confines of the gravity

A blob of photons that forms a black hole will have pressure, yes; but if the photons have formed a black hole, the pressure can't have been sufficient to overcome the gravity of the photons. If it were, a black hole would never form in the first place. Once the hole forms, the pressure of the photons will never overcome their gravity, and all the photons will fall into the singularity and be destroyed. (At least, that's what happens in the purely classical model of black holes; if we throw in quantum effects like evaporation, things become more complicated--see below.)

at a certain distance from the singularity the photon pressure with overcome the gravity

No, because, as above, if pressure is sufficient to overcome gravity, the photons will never form a black hole in the first place, so what's at the center won't be a singularity; it will just be the center of an ordinary blob of photons whose contraction will be stopped by the pressure of the photons, and which will then start expanding again.

if a black hole shrinks through evaporation, there will come a point when the photon pressure will supersede the event horizon

No, there won't. Adding quantum effects like evaporation does make things more complicated, as I said above, but it doesn't make the inside of a black hole any more like an ordinary "container" of photons or anything else.

There are basically three possibilities for what happens when we take the classical model of a black hole, in which the hole is "eternal" and can never lose mass or evaporate away, and add quantum effects like Hawking radiation.

(1) Quantum effects prevent a black hole from ever forming in the first place; no actual event horizon ever forms. Compact objects that look, from the outside, very much like a black hole might still form (in more technical language, an "apparent horizon", where radially outgoing light no longer moves outward, might still form), but they would not actually be black holes (for example, any apparent horizon that did form would eventually disappear, so there would be no permanent boundary preventing light or other things from escaping). What we call "black hole evaporation" on this model would actually be generated by apparent horizons, not event horizons, and would tend to eventually make them disappear, allowing objects that fell inside those apparent horizons to escape out again.

(2) Quantum effects allow an actual black hole to form (i.e., they allow actual event horizons to form, so that objects inside them never escape), but do not allow a singularity to form at the center. Thus, objects that fall through the event horizon, although they can never actually escape back out, do not get destroyed in a singularity. On some versions of this kind of model, the objects that fall in enter a new "baby universe" that gets spawned when the hole is created; on other versions, it's not entirely clear what happens to them (and that is one reason why this group of models is probably not workable). A black hole that forms can eventually evaporate, and the radiation that comes out during the evaporation can, at least in some versions of this kind of model, contain all the information about objects that fell in, even though the objects themselves can't escape back out (they don't even come out if the hole finally evaporates away completely).

(3) Quantum effects allow an actual black hole to form (i.e., they allow actual event horizons to form), and a singularity forms at the center of each black hole. A black hole can eventually evaporate, but anything that fell into it while it existed gets destroyed in the singularity. On some versions of this kind of model, the radiation emitted during the evaporation process somehow contains all the quantum information that was in the objects that fell in (but in highly scrambled form so it's practically impossible to reconstruct the objects from the information). On other versions, that quantum information is lost when the objects hit the singularity and are destroyed.

Possibility #1 makes the whole question we are discussing here moot. Possibilities #2 and #3, as you can see, do not allow anything like photon pressure overcoming the hole's gravity, and do not make the hole anything like an ordinary container or object.

 

[PeterDonis]

if the black hole formed the photons would be trapped inside falling toward the singularity. They would lose their sense of being photons as only their properties of mass, charge, and angular momentum are preserved...

That's not correct. The "no hair" theorem only applies to the hole itself, as seen from outside. It doesn't apply to individual objects that fall inside. Those objects might get destroyed in the singularity (depending on which model we are talking about--see my previous post), but until they do, they retain all the properties (like what kind of particles they are) that they had outside the hole.

 

[jedishrfu]

Thanks for the clarification, now I know why I'm losing my hair.

I guess I was confused by the wiki article that says once they fall past the event horizon the theorem applies:

http://en.wikipedia.org/wiki/No-hair_theorem

 

[PeterDonis]

the wiki article that says once they fall past the event horizon the theorem applies

The article says that the holes themselves are indistinguishable "to an observer outside the event horizon". Such an observer can't see anything inside the horizon anyway, so he can't tell whether there's matter or antimatter there falling into the singularity (or what kinds of matter or antimatter particles are there). I don't see anywhere that the article says the individual particles that form the hole "lose their identity" inside the hole; it only talks about the global characteristics of the hole itself, as seen from outside the horizon.