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I may be asking this is a profoundly stupid way but I'm not that knowledgeable when it comes to quantum mechanics.

It's well understood that time dilation occurs around any area that has mass but it isn't significant unless the mass is sufficiently large. This causes the relative movement of local time to appear to travel at a slower rate than other areas when observed from outside of the field of influence.

I'm curious to know if time dilation affects the matter that causes the dilation in the first place. For example, if there a massive amount of a radioactive isotope that is actively decaying at a set and known rate and it is large enough to warp time, relatively speaking, will it appear from very far off that the radioactive isotope is decaying at a slower rate? I know that, locally, the rate appears to be the same but I'm asking from the point of observation that is outside of the gravity well.

I hope this isn't too confusing. If so, leave a comment and I can try my best to elaborate.

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A couple of ways of looking at this. The first one is that gravity is self interacting -- the equations of General Relativity are nonlinear, and obtaining solutions involves having all the higher order effects taken into account. Any matter energy can interact with any other matter energy gravitationally. In a posible quantum description of gravity (which we still don't know how to so, but in the simplest semi linearized view) even the gravitationa quanta, the gravitons, will interact with each other. It can get pretty complicated.

The other way is to imagine some cases where we have already obtained solutions, and examine whether they provide an answer. One example is black holes (BHs). As BHs are getting formed y collapsing exploded supernova the matter will be pulled into a tighter and tighter volume. As it does the gravity outside it keeps getting stronger. As the matter approaches the horizon, the gravity gets even stronger, and the time dilation (for an observer far away, as you asked), increases without limit and approaches infinity. Thus an observer far away sees the collapse slowing down, and never sees the matter going into the horizon. Another way of saying it is that a far away observer will never see the BH fully collapse inside its horizon. The BH collapsing causes the time dilation, and suffers it for an observer far away.

An observer falling in with the matter will not experience any time dilation, and after a finite time finds himself/herself inside the horizon, without even knowing he/she went through it. And can never escape. He/she, in a very short time, falls towards the singularity, gets very deformed and well, falls into the sigularity (or whatever quantum entity replaces it in a quantum theory of gravity).

Now, the large dilation happens, for an outside observer, much more strongly as the infalling matter approaches the horizon, where velocities are high and the actual collapse happens very fast for the infalling observer. For the far off observer, even with time dilation, it is still fast, and they would see the horizon being approached, and then sees nothing of the infalling matter or observer. So, even if it is an 'almost BH', there are no observable differences. The two BHs that merged and we observed it's gravitational radiation in 2015, we saw them merge in their last few orbits around each other in less than a second. That's why there are so many BHs in the universe, we believe, they are 'almost BHs', but for us ther is no observable difference.

So, yes, in any region in spacetime the gravitation is described by the curvature of the spacetime, and will affect anything there.

What of a single elementary particle, does its gravity affect it? We think it has to in some self consistent way to allow the particle to be what it is, but we still,have not developed an accepted theory of quantum gravity. When we try to use the normal rules of quantum theory to figure out those self effects, we get infinity. And unlike in quantum field theory where we have figured how to deal with those infinities to get finite results, we don't know how to do that in quantum gravity. It is what is called a non-renormalizable theory. So, we don't know the answer at the quantum level.

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  • $\begingroup$ I don't quite understand why the core of a star, while it is collapsing into a singularity, tends to grow a stronger gravitational field. If massive particles warp spacetime, then why would the gravity well change if no more matter is added? Density, as I recall, is the same amount of matter in a set volume but it's still the same amount. If there are two objects that have the same amount of matter but have a density delta, would they have the same gravitational field? $\endgroup$ – Rincewind Mar 8 '17 at 5:39
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    $\begingroup$ The matter gets into a tighter ball (or so), so on the 1/r type force (in GR similar type singularity at the origin, and different effect, the horizon at the horizon) the r is pretty small and you have a very large force. Really needs GR to describe it well but at the horizon the metric term for the dilation effect for an observer at infinity is infinite $\endgroup$ – Bob Bee Mar 8 '17 at 19:23
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    $\begingroup$ And it is true that at distances like ours to the Sun, the force of gravity of a black hole would just be the same as any star of the same mass. The horizon is just a few Kms from the center, and all the mass is inside, so to speak $\endgroup$ – Bob Bee Mar 9 '17 at 2:39
  • $\begingroup$ Seeing the 1/R relationship definitely cleared it up for me. I didn't know that gravity worked in that way. I figured it is stronger near the center of a spherical object but it doesn't increase because the matter doesn't increase. However, if the radius is reduced (it becomes more dense), gravity increases until a limit is reached (eg PEP). Thanks! $\endgroup$ – Rincewind Mar 12 '17 at 3:49

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