Posted on 02/23/2023 12:56:12 PM PST by Red Badger
Shopping!....................
Just the fact that some black holes are larger than others indicates that there is some theoretical limit to their size.
At some point, the intense gravitational forces compacting the masses that fall past the event horizon, will reach a ‘critical mass’ where they will no longer be able to compress the incoming mass, and will ‘let go’ when more mass is added.
There must be a formula for this........................
In the reporting I’ve seen, I’d rather call it looting.
Do we even know what a black hole is?
Well, yes and no. We know that it is a region of such great energy density that it has a gravitational field so great that nothing that passes a certain distance from the center of it (known as the event horizon) can escape. So that’s the yes part. In the equivalent terms expressed in the language of relativity, it is a region of highly curved spacetime such that the ordinarily space-like coordinate that describes the distance from the black hole center becomes a time-like coordinate instead. This means that not only can nothing escape once it crosses the event horizon, it cannot move freely in any spatial direction, but instead is constrained to fall ever closer to the center. Essentially anything crossing the events horizon falls forever.
That’s the “yes” part. We can make these conclusions based on the Einstein field equations of General Relativity, so we are fairly confident in them. Not only do observations such as these conform to what is predicted by GR, ALL observations of systems in which gravity plays a significant role conform to the predictions of General Relativity. There are no exceptions (as of now). The consequences of GR seem weird, but that is because our normal experience is in an environment where an approximation to them, namely Newtonian gravity, holds to a high degree of accuracy. While the two agree in most everyday situations, there are measurable (but not immediately apparent) effects where they differ, and in all such cases relativity gives the right answer.
Two good examples: very accurate clocks will show different times on earth and in a weaker gravitational field in orbit. This is accounted for by relativity and absent n Newtonian gravity. We know it occurs because our GPS systems require very accurate time measurements to give accurate locations, and the clocks in these systems must be adjusted to account for the gravitational field in the GPS satellites. Another example, if you stand on the ground and shine a light toward the top of a tall building, the light will have a different color when it gets there than it did when it started out. The light will be redder at the top of the building - that is it will have a lower frequency. This effect is too small (and our buildings are too short) to observe.with visible light, but it has been measured with gamma radiation (which has a higher frequency and thus a greater effect).
Now the “no” part. Since nothing can escape from the event horizon, we cannot observe anything inside it. We cannot tell what black holes are made of. We cannot tell what is happening to anything inside the horizon. The observations about curved spacetime and objects being forced to fall forever are from the reference frame of an outside observer. The equations of relativity, as confident as we are about them, simply cannot be applied to the region inside the event horizon in a sensible way. It is fair to say that we don’t know what is inside the black hole. As it turns out, all we can tell about a black hole is its mass, electrical charge and angular momentum. Anything else is impossible to know.
There is a formula, but it does not give an upper limit to the size or mass of a black hole. A black hole is any object smaller than its Schwarzschild radius, which is given by 2GM/c^2, where G is the gravitational constant and c the speed of light. Since (are my previous post) we cannot tell what happens inside the event horizon (anything closer than the Scwarzschild radius), the only sensible size we can attribute to a black hole is this value.
Therefore adding more mass to the black hole does not compress anything further. The radius of the black hole increases linearly with increasing mass. This is quite different than ordinary objects where the volume of the object increases linearly with mass. For ordinary objects this implies a constant density since mass and volume increase in proportion. For black holes the volume increases as the third power of mass (volume is proportional to the third power of the radius, which is directly proportional to mass). Because of this, the mass density of a black hole DECREASES with increased mass - it becomes less compressed, not more.
So, it gets fatter and fatter as more mass accumulates until the event horizon becomes full, and if more mass comes in it pops like a soap bubble?...................
Nope. More mass just makes it keep getting larger. It is pretty interesting (coincidence?) that the Schwarzschild radius of a black hole with the mass of the observable universe is pretty close to the actual radius of the observable universe. That is a black hole with the same mass as everything we can observe would be approximately the same size as what we observe, leading to the question- Do we actually live inside a black hole? This possibility is studied seriously by some theoretical physicists and can actually explain the expansion of the universe from a minimum size.
It’s hard to see, however, how this possibility could ever be confirmed (or refuted) observationally.
Everything that we can see is not all that there is to see...................
Thanks for your well-informed, reasoned considerable and considerate response. You managed to give some definition to an indefinite phenomenon. It was very kind of you.
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