A simple argument against the formation of singularities runs as follows:

1) Hawking radiation has a temperature T, proportional to 1/R where R is the radius of a black hole event horizon, but the horizon is not a real boundary, so the Hawking effect and effective temperature presumably continues to operate as one travels down towards the center of the hole.

2) The amount of energy produced by a black body at a given temperature is proportional to T**4 and exerts the same outward pressure on incoming particles as that which balances gravity in our sun.

3) If T is portional to 1/R and if the amount of energy produced is proportional to T**4, we will experience a repulsive force proportional to 1/R**4 which will eventually balance a gravitational pull that only increases at 1/R**2 and we will reach equilibrium. As incoming matter stops before reaching the hole center, no singularity ever forms.

This argument also provides cut-off-distance that allows gravity to be combined with ordinary quantum mechanics without encountering singularities.

Of course, it all hinges on the choice we made in (1) to use a formulation where T depends on 1/R, rather than depending on 1/M where M is the mass of the hole.

If this is the reason why it is invalid, it must be that the process which generates Hawking radiation at a particular spot on the radius of the event horizon is not dependent on the radius of curvature at that point, but on some other characteristic that distinguishes the hole at that point from one on another hole of different mass. If so, what property is this? If not, what exactly is the error in the above argument?
prometheus
There is an error in point 1: "the Hawking effect and effective temperature presumably continues to operate as one travels down towards the center of the hole."

Even if particles were "created" inside the black hole their mass would be retained by the black hole since a particle inside a black hole must hit the singularity some finite time in the future. The black hole can only lose mass by particles created at the event horizon.
You make a reasonable point, but it is one that applies equally to Hawking radiation formed at the event horizon. In order for it to have a non-zero frequency away from the horizon, it must have had an an infinite frequency at the horizon due to the Doppler shift. Yet, Hawking radiation is as well accepted as the Unruh effect and the Sokolov-Ternov effect.

Another way of looking at it is to consider a pair of photons, P1,P2 as shown below

Black Hole Center <---P1 P2---> <----Traveler

Even though the force of gravity may cause P2 to fall towards the center relative to an observer outside the event horizon, its speed relative to the Traveler is unchanged at 3 * 10 **8 m/s, as is it's frequency.

Please note that my argument does not suggest that the black hole will lose mass from "internal" Hawking radiation, and incoming matter will still cause the hole to grow until the universe grows cold, all it does it prevent the formation of a singularity inside the hole.
Sapo
What is it you misunderstand?!!!

Oh, for God's sake...
yor_on
What do you mean by this?
" but the horizon is not a real boundary, so the Hawking effect and effective temperature presumably continues to operate as one travels down towards the center of the hole."

Are you saying that you are expecting Hawking radiation all the way 'down'?
I thought that was a 'spin off' at the 'event horizon'???

And that the 'event horizon' was at a 'fixed distance' dependent on the 'mass' of black hole.
Which changes dynamically as new thingies come in and say hi:)...
You asked if I am saying that Hawking radiation continues all the way down and the answer is Yes, that is exactly what I am saying and it is the crux of the entire argument.

To be exact, I am saying that just as Hawking radiation at the horizon matches the Unruh effect experienced by an observer subject to an equivalent acceleration, an observer diving towards the hole center will experience an ever-increasing level of Hawking radiation that is proportional to the gravitation pull at their current distance from the center.

yor_on
As far as I'm getting it the hawking radiations is a 'byproduct' of virtual particle pairs.
As no one have seen it we don't even know if it will be a 'glow' around a black hole.

Is it this you are referring to when you think about it?
"The usual computation involves Bogoliubov transformations. The idea is that when you quantize (say) the electromagnetic field you take solutions of the classical equations (Maxwell's equations) and write them as a linear combination of positive-frequency and negative-frequency parts.

Roughly speaking, one gives you particles and the other gives you antiparticles. More subtly, this splitting is implicit in the very definition of the vacuum of the quantum version of the theory! In other words, if you do the splitting one way, and I do the splitting another way, our notion of which state is the vacuum may disagree! "

In what way would your idea disprove 'the formation of singularities'.
And i take that as you are referring to the 'creation' of a black hole..

As for if it's only glowing at the 'event horizon' I don't know, as there seem as no perfect 'real life' analogy of this mathematical proof exist.

-----------------------------

Just a thought :)
It's a geodesic path of least resistance

And you mean that those virtual pairs somehow won't negate out themselves and become a 'ocean' thick enough to brake the movement of those 'thingies'
But won't they to have a mass as they when existing will no longer be 'virtual'?
Or are you expecting them to consist of some kind of antiparticles with a negative mass? repulsing particles or anihilating them (and the Black hole then?)??
I don't get this..
Hey :)
No surprise here right...
Latrosicarius
QUOTE (ColinConrad+Apr 12 2008, 12:44 AM)
but the horizon is not a real boundary, so the Hawking effect and effective temperature presumably continues to operate as one travels down towards the center of the hole.

the temperature of hawking radiation is what is supposedly seen radiating from event horizon. However, it's far hotter on the inside.

QUOTE (ColinConrad+Apr 12 2008, 12:44 AM)
Of course, it all hinges on the choice we made in (1) to use a formulation where T depends on 1/R, rather than depending on 1/M where M is the mass of the hole.

Because R is proportional to M
prometheus
QUOTE (Latrosicarius+Apr 14 2008, 05:24 PM)
the temperature of hawking radiation is what is supposedly seen radiating from event horizon. However, it's far hotter on the inside.

It doesn't matter how hot the radiation inside the hole is because it won't cause any change in the black hole whatsoever.
yor_on
Latrosicarius How would that temperature express itself (inside the event horizon) when viewed from the 'outside' (the observer)?
Inside time will adapt to the 'objects' right. The gravity has to rise the closer one come to the core. Otherwise no objects ever would move in...
That must mean that time as seen from the outside will slow down even more the closer to the 'core'.
So how would the temperature been seen from a thought 'observer'
Isn't it also so that if we would imitate Jules and move in to the exact middle of our Earth the gravity in there would be null?
Would that be the same for a black hole??

The inside would have no temperature as we would observe right? as well as no motion.
The next question is how strong/big can it become.
Can it totally stop time as seen from us.
It should not be possible as long as it participate with space time?
Because if it does we can not say anything about what happens inside that 'event horizon' right?
Very strange subject, black holes :)

Lastly relating to the possible size of a black hole
What would the space distortion be inside such a one
Depending on size? limitless space?
Latrosicarius
Yes, it doesn't matter how hot it is on the inside from an outside observer. They won't be able to tell.

If the black hole is a singularity, the event horizon will increase its radius proportional to mass (obviously).

If the black hole is not a singularity, but instead is a rotating sphere of degenerate matter, the event horizon will still increase its radius proportional to mass. However, if you were able to look inside of the event horizon, you will see the diameter of the sphere contracting as more mass is added.

And actually, since it would be rotating at almost the speed of light, it would technically not be a "sphere", but an oblate spheroid, as the diameter of the equator is wider than the diameter through the poles.
yor_on
:) Thanks.
StevenA
QUOTE
A Reason Why Singularities Do Not Form

There was, from the beginning, no reason other than invalid mathematical assumptions that singularities should have formed. It was the mathematical models, of continuous and undifferentiable spaces, that contained informational black holes and these models haven't been shown to correlate to detailed properties in physics, because space is constructed from information and not visa versa.

The basic problem is that probably more than half of the mathematics that was used to derive black holes was based upon physical intuition disguished as "logic" and obviously physical intuition of nearness, proximity and convergence etc. is quite lacking with respected to deterministic logic (not that all of physics is ruled by deterministic logic, but the comprehensibly useful components of it are). Einstein himself couldn't do much more than try to pawn off the paradoxes in manner that created paradoxes themselves (the probability of getting lucky and making a correct prediction on a subject that no information has been retained is quite small - the single problem of having both gravity and light travel at the same speed, yet black holes "suck" in light, via gravity, but not gravity itself, is an obvious problem that shouldn't take more than a single presentation to recognize the problem).

So basically the "real" numbers and continuous field theories have been flawed from the start and it's simply most pronounced when applied to phyiscally extreme conditions (of which the result ends up as effectively "does not compute").

Continuous field theories are simply approximations based upon human intuition and subconsious processes and they will be replaced with informational models that don't round everything into insignificance, but it appears we'll have a century old legacy to overcome first.
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