a black hole is first large object until it has enough mass to make it inescapable. Once the black hole accumulates the amount of mass to make it inescapable, doesn't time stop down for that mass that keeps accumulating after that point?
Whether something is a black hole not has nothing to do with the mass. The mass of a grain of salt could be a black hole as well. Actually the amount of matter is not relevant, it is the ratio between area and mass that matters. A non-spinning object becomes (or is already) a black hole if the ratio between the area it occupies and the area that represents its mass is smaller than 4. As soon as this happens the object's occupied area will shrink to zero. E.g.: [tex] {A_{occupied} \over A_{mass} } < 4 [/tex]
Passionflower, you may want to clearly define "area occupied" since most people will think in terms of "volume occupied".
Actually I think it is simpler to express it in terms of area as volume is not Euclidean in curved spacetime and it avoids the usage of the r coordinate which is not a measure of distance in Schwarszschild coordinates. For instance the volume occupied from the EH down to the singularity is actually infinite so that is not very helpful.
I agree it is simpler, but you still should explain what it means for a mass to occupy an area just for clarity. Most new posters will not know what you mean.
black hole and time stopping are far off . time stops relative to things outside it. And center of a black hole is a point of infinite density and zero volume . mass has to do with the size of black hole . it doesn't acquire mass it shrinks to zero volume making everything inescapable.
Are you sure about that? I thought that ring singularities were 1 dimensional. So they would have a circumference, but no volume. But I admit that I have not studied the Kerr solution in as much detail as I should have.
But some black holes have less mass than those huge stars, you might have some misunderstanding. And what do you mean by "time stop down for that mass"?
Zeal, I didn't state my question very well. Rather than say "When a mass gets big enough" i should have said "when a mass qualifies as a black hole". sorry. Anyhow i was just trying to understand better what is going on with the mass as it goes from not being a black hole to being a black hole. I guess time slows down gradually for the mass as it accumulates. Correct me if i'm wrong. Thank you.
The time slowing/stopping is from the perspective of the outside observer. For matter flowing into the singularlity time flows from its perspective as normal.
I think that going from normal stars to black holes is usually very rapid, which involves super nova explosion or collapse of giant stars. Using the Schwarzchild black hole as the simplest model, you can see that it is the radius that matters. To my perspective, if the radius of the event horizon is smaller than that of the star, it would not be a black hole. But usually collapse of stars and super nova explosion cause these rapid decrease of radius.
Gravitation potential becomes lower as we go toward center of mass. Because of that event horizon should first form at the center of gravitating body that is going to turn into the black hole and then move outward. I believe that is the way how birth of BH is modeled. But at the center of gravitating body mass is not falling anywhere. So it should be extremely time dilated right before it turns into the black hole. So from where this "seed" black hole appears at the center of the body?
You might find the following post (and the thread) from this thread of interest (Note: M=Gm/c^{2})- *It's worth noting that in GR, pressure contributes to the stress energy tensor so the more compact a neutron star becomes, the greater the gravity.
And why exactly r_{0} will be gradually reduced? To me it seems the other way around - that r_{0} should gradually increase. First, additional matter occupies some place and second, kinetic energy of accreted matter is converted into heat that would tend to expand the body.
The kinetic energy would convert into pressure (sometimes, pressure is described as confined KE) and Einstein's algebraic equation for gravity is [itex]g=\rho+3P[/itex] where [itex]\rho[/itex] is density and P is pressure and so the gravity would increase, pulling the star in on itself.
Fine, confined KE will contribute to gravity by tiny bit so that expansion will be reduced by tiny bit but summary effect will be expansion not contraction.
Can you provide equations or proof that demonstrates this. The common census is that as a neutron star increases in mass, it's radius reduces.
I'm having a discussion with zonde about a similar point in another thread; I posted this earlier today: https://www.physicsforums.com/showpost.php?p=3497951&postcount=26 in which I reminded myself and zonde that a self-gravitating body has a negative heat capacity. That means that if you add energy to it, it expands and cools (i.e., its temperature goes *down*, not up), and if you take energy away from it, it contracts and heats up (i.e., its temperature goes *up*, not down). In other words, increasing the temperature of such a body does *not* create a tendency to expand against gravity. Similar reasoning applies to the case under discussion here; the only difference is that, for an object above the maximum possible mass for a neutron star (the TOV limit), it will collapse even if it is not radiating away any energy to the outside universe. But that doesn't change the fact that the increasing temperature as it contracts does *not* compensate for the increased gravity that is pulling it in.