black hole question

Jonny_trigonometry

The event horizon is just the radial distance from the center of mass where the speed of light is the escape velocity, and the radius of the object does not extend beyond this radius. Then all particles have an event horizon by that definition if you solve with newtonian gravity, so that makes me ask a question. Is there some radial distance and/or some mass where GR fails to compute the even horizon? Does this have anything to do with the uncertainty principle?

Danger

My contention here is that you cannot assemble that much mass in one place without it collapsing into a singularity due to its own gravity.

Can't help with your question, Jonny. It's way beyond me.

pervect

Microsoft provides a power-point viewer

http://www.microsoft.com/downloads/d...displaylang=en

which works fine with the link Hellfire provided.

http://www.physics.nus.edu.sg/einste...t10/lect10.ppt

pervect

Note that this doesn't mean a strong "field". A very weak field that does not drop off with distance can also trap light. That's one of the weaknesses in the dictionary defintion you posted, it's a bit misleading on this point. Thinking about the "escape velocity" being greater than or equal to 'c' gives a less misleading picture than your dictionary defintion.

So far so good.

There are reasons for beliving that normal matter cannot support a pressure (force/unit area, energy/unit volume) greater than c^2 times its density (mass/unit volume). The c^2 is a unit conversion factor. This is known as the "strong energy condition" and comes from requiring that the energy density term in the stress-energy tensor always be positive in any frame of reference.

What the singularity theorem says is that assuming the strong energy condition is true, matter can not be strong enough (have a high enough pressure) to keep itself from collapsing under its own weight when you collect enough of it together to form an event horizon (black hole).

Because pressure cannot halt the collapse, the final state of any such collection of matter will be a singularity.

franznietzsche

The thing is, its physically impossible for that much matter in that little space to not collapse into a singularity.

What you're describing is not physically possible. The amount of matter necessary to generate an event horizon will always collapse into a singularity.

You're trying to apply newtonian thinking to a strictly non-newtonian problem. Essentially high school physics to what is a grad school level problem.

You cannot use newtonian gravity with black holes. Period. It fails, completely in that regime. If you tried to calculate even horizons you suggest you would get event horizons inside the particles, which would be wrong, since once you're inside an object, the standard gravitation force equation no longer applies and the situation is much more complex. This has nothing to do with the uncertainty principle. You cannot use newtonian gravity to calculate things in General Relativity regime. Its like explaining how humans walk with their wings. It just doesn't make any sense. The two are based on drastically different assumptions, and are only in agreement when those differences are negligible. Black holes are a phenomenon where they are definitely NOT negligible.

And as Danger pointed out its not really correct (Wow, Danger you just keep impressing me more and more with what you've learned here).

Yes

Yes
Yes, but poorly worded. Sufficient matter can bend space enough to trap light. However, that must occur outside of the object, as the gravitational field weakens once you are inside of an object (because some of the mass pulls outward, not inward).

Yes
No. Singularites are mandated by the same principles that make the previous statements true. if those are true (in the form of our current theories) singularities have to exist. And by those same theories, only the singularity can form the even horizon. You are trying to seperate things that are closely linked. The fact that a singularity is the only thing that can produce an event horizon is a consequence of the same things that make the above statements true. So if the above statements are true (or rather, if our theoretical derivation of them is true, meaning we didn't get the right answer the wrong way, like Bohr did) then only singularities can produce event horizons.

Yes.

Danger

Thanks.
I have learned a tremendous amount about almost everything since joining. Actually, though, this isn't one of them. I wrote a technical article on black holes for a major newspaper in '79. Unfortunately, I've forgotten most of what I knew then.