I Gravitational Influence: Limits & GR Effects

[Leonardo Muzzi]

As I understand, under Newtonian Gravity, there are no limits for the length of the gravitational influence of an object, except the speed of causality and the age of that object. So, considering the Sun as an example, which is roughly 4.6 billion years old, its gravitational influence would expand for 4.6 billion light-years.

Of course, that scenario considers the Sun just appeared out of nowhere. Considering the matter that originated the Sun was there before it became a star, the Sun gravitational influence would possibly expands to the whole Universe.

How that works under General Relativity? Considering the existence of Dark Energy, and any other stuff of GR meaningful to the question, would the limits of the gravitational influence of objects be different?

 

[NFuller]

Under Newtonian gravity, the range of the gravitational field is infinity and the gravitational field propagates instantaneously. There is no "speed of causality" in Newtonian mechanics. In GR, gravitational changes propagate through space at the speed of light.

 

[Leonardo Muzzi]

Under Newtonian gravity, the range of the gravitational field is infinity and the gravitational field propagates instantaneously. There is no "speed of causality" in Newtonian mechanics. In GR, gravitational changes propagate through space at the speed of light.

But in GR is the gravitational field also infinite?

 

[NFuller]

Only if it has infinite time to propagate, so generally speaking no.

 

[Leonardo Muzzi]

Only if it has infinite time to propagate, so generally speaking no.

Right! So besides the speed of light + time limit, there is nothing that limits a gravitational field?

I am thinking about some kind of anti-gravity, dark energy effect, that would prevent a gravitational field from propagating infinitely.

After all, if dark energy flattens the Universe, doesn't that mean it cancels out the effects of gravitational fields at longer distances, otherwise the Universe would be curved?

 

[PeterDonis]

I am thinking about some kind of anti-gravity, dark energy effect, that would prevent a gravitational field from propagating infinitely.

Any such effect would not "prevent" a gravitational field from propagating, because any such effect would show up as an effect on spacetime curvature, and spacetime curvature is the "gravitational field", at least in the sense in which anything can be said to "propagate" in GR.

 

[NFuller]

I am thinking about some kind of anti-gravity, dark energy effect, that would prevent a gravitational field from propagating infinitely.

After all, if dark energy flattens the Universe, doesn't that mean it cancels out the effects of gravitational fields at longer distances, otherwise the Universe would be curved?

I don't think anyone knows the answer to that. Dark energy is not understood in any sense, we don't even know if it exists. Some scientists subscribe to the idea that there is some unknown force or energy that is accelerating the expansion of the universe while others assume that our theory of gravity is incomplete and that this is the cause of the discrepancy. I personally lean towards the latter here.

 

[PeterDonis]

if dark energy flattens the Universe, doesn't that mean it cancels out the effects of gravitational fields at longer distances, otherwise the Universe would be curved?

Dark energy does not "flatten" the universe. It produces spacetime curvature that is different from the kind produced by ordinary matter and energy, but they don't "cancel each other out" to produce flat spacetime.

You will see cosmologists talking about the universe being "flat", but they mean spatially flat, not flat spacetime. The universe is observed to be spatially flat as best we can tell with our current instruments, and that requires the total energy density (counting dark energy, dark matter, and ordinary matter and radiation) to have a particular value; but that doesn't mean dark energy flattens the universe.

 

[NFuller]

Dark energy does not "flatten" the universe. It produces spacetime curvature that is different from the kind produced by ordinary matter and energy, but they don't "cancel each other out" to produce flat spacetime.

I think the OP is trying to ask if gravity may be attenuated differently at very large distance scales than it is at smaller scales. Maybe some clarification would help?

 

[Leonardo Muzzi]

I think the OP is trying to ask if gravity may be attenuated differently at very large distance scales than it is at smaller scales. Maybe some clarification would help?

Yes fair enough!

So to rephrase it: In Newtonian physics, if I take an empty Universe and put two Suns perfectly still to each other, 13 Billion light-years away, the gravitational fields of each will affect and attract the other.

Is that still true in GR?

 

[PeterDonis]

Is that still true in GR?

Yes.

 

[Khashishi]

You can't just make Suns appear out of nothing. They have to be constructed from stuff from nearby locations. The gravity between two stars separated by large distance is due to the gravity of the stuff which existed near the stars location in the past.