Where Does Earth's Counter Gravity Go in an Expanding Universe?

[James Alton]

The external field of a black hole is not "generated" from inside the horizon. It is "generated" from the far past when some object originally collapsed to form the hole. (A better way of phrasing "generated" would be "determined using the Einstein Field Equation"; the EFE says that the curvature of spacetime at a given event is determined by the stress-energy present in the past light cone of that event. Even after an object has collapsed to form a black hole, the past light cone of events outside the hole still contains the history of the collapsing matter, and that history is what determines the hole's field.)

Peter,
Thanks for your input. So if I understand you correctly, the mass of the hole has not changed after the collapse, therefore the field that existed prior to the collapse is static, like an "imprint" on space time. I would be fine with this if the holes were stationary but when they are in motion it is not clear to me to me how the information between a hole and another object is being updated.

The speed of gravity is the same as the speed of light c

The external field of a black hole is not "generated" from inside the horizon. It is "generated" from the far past when some object originally collapsed to form the hole. (A better way of phrasing "generated" would be "determined using the Einstein Field Equation"; the EFE says that the curvature of spacetime at a given event is determined by the stress-energy present in the past light cone of that event. Even after an object has collapsed to form a black hole, the past light cone of events outside the hole still contains the history of the collapsing matter, and that history is what determines the hole's field.)

 

[PeterDonis]

the mass of the hole has not changed after the collapse, therefore the field that existed prior to the collapse is static, like an "imprint" on space time.

This is true for the idealized case of a single spherically symmetric mass collapsing to a non-rotating black hole that never has anything else fall in. For the more general case, the field will not be static, but it will still be determined by the presence of stress-energy in the past light cone.

when they are in motion it is not clear to me to me how the information between a hole and another object is being updated.

If the holes are in motion, it's because the matter that collapsed to form them was in motion. It's still the same principle: the information doesn't have to come from inside the holes, it comes from the matter that collapsed to form them.

 

[James Alton]

This is true for the idealized case of a single spherically symmetric mass collapsing to a non-rotating black hole that never has anything else fall in. For the more general case, the field will not be static, but it will still be determined by the presence of stress-energy in the past light cone.
If the holes are in motion, it's because the matter that collapsed to form them was in motion. It's still the same principle: the information doesn't have to come from inside the holes, it comes from the matter that collapsed to form them.

Ok, so the gravitational field of a black hole does update based on any additional mass being added. The mass hidden behind the event horizon if added to comes from mass that was outside of the light cone so the accounting makes sense to me in this regard. As to the motion however, galaxies collide and all sort of events could potentially alter the motion of a hole over time. Does the field update based on these changes in motion (even though some portion of the mass is hidden behind an event horizon) just as any other object? If so how? Thanks, James

 

[PeterDonis]

all sort of events could potentially alter the motion of a hole over time. Does the field update based on these changes in motion

Sure, because any change in the motion of the hole will be driven by the behavior of mass somewhere outside its horizon.

 

[Chalnoth]

Ok, so the gravitational field of a black hole does update based on any additional mass being added. The mass hidden behind the event horizon if added to comes from mass that was outside of the light cone so the accounting makes sense to me in this regard. As to the motion however, galaxies collide and all sort of events could potentially alter the motion of a hole over time. Does the field update based on these changes in motion (even though some portion of the mass is hidden behind an event horizon) just as any other object? If so how? Thanks, James

An overly-simplified way of stating it is that the field updates at speed c, as gravity waves propagate the changes through the field.

The more complicated way of saying this is that some apparent changes to the field don't need any updates, and so appear to propagate instantaneously. To see how this might work, consider linear motion. With regard to linear motion, simple consistency requires that if we want the gravitational field of a black hole moving linearly, that field must be identical to the field we get from simply taking the black hole's space-time, and transforming to coordinates that are moving with respect to the black hole. This requirement ensures that an object near a moving black hole will be pulled towards the center of the black hole, not towards the position it was 7 minutes ago if the black hole is 7 light minutes away.

It turns out that when you work through the math, gravity not only doesn't need to update for linear motion, but it also doesn't need to update the field for acceleration.

Changes in acceleration, however, need to update, and an object which is changing its acceleration will radiate gravity waves (though typically very, very little unless the change in acceleration is massive, such as for an object very close to a neutron star or black hole).

 

[Chalnoth]

Somewhat related to this topic, here's a really cool simulation of the merger of two black holes:


What you're seeing here is a visualization of the event horizon, with the colors indicating the curvature scalar at the various points (it's different around the equator of the black hole because it's spinning).

What's really interesting here is that the event horizon distorts when the merger takes place. Throughout this process, the pair emits gravity waves, and this continues until the final black hole relaxes into its final shape (which takes very, very little time after the two black holes touch).

 

[James Alton]

Sure, because any change in the motion of the hole will be driven by the behavior of mass somewhere outside its horizon.

Peter, Going to have to think some more on this one but I really appreciate your input. James

 

[AgentSmith]

Yes. But that pressure has no direct impact on expansion. However, pressure also acts as a source of the gravitational field, so that it impacts how gravity behaves.

This is probably made clearest by considering a box containing a negative-pressure substance, with zero pressure outside the box. The pressure would be pulling the sides of the box inward.

I think talking about the cosmological constant in terms of the pressure can be confusing. The simplest way to think of it is this: the curvature of the universe is a function of how much stuff there is in the universe. It manifests itself as the rate of expansion. Because the cosmological constant is constant, you get the same amount of stuff at all times, which means the curvature is constant, which means the rate of expansion is constant. A constant rate of expansion leads to exponential growth of the distances between objects.

But the rate of expansion is not constant, it is accelerating.

 

[AgentSmith]

It's still described as a force. General relativity doesn't change the usage of this term.

True, but the usage is habit, just as we talk about centrifugal force in basic physics, but in more advanced mechanics courses is referred to as a pseudo- force, with explanation of course. Then we all go right on talking about centrifugal force.

 

[Chalnoth]

But the rate of expansion is not constant, it is accelerating.

The rate of expansion is usually defined as $\dot{a}/a$. This rate is currently decreasing and seems to be approaching a constant value (proportional to the square root of the cosmological constant). When you have a differential equation given by:

{\dot{a} \over a} = H_0

where $H_0$ is a constant, then $a(t)$ has exponential growth. The solution is:

a(t) = a(0) e^{H_0 t}

So it's not the rate of expansion that is accelerating, but the distances between objects.

 

[Chalnoth]

True, but the usage is habit, just as we talk about centrifugal force in basic physics, but in more advanced mechanics courses is referred to as a pseudo- force, with explanation of course. Then we all go right on talking about centrifugal force.

It's usually the other way around. In basic classes, people usually talk about centripetal forces, which are so-called "real" forces. The centrifugal force is usually not dealt with until you get to pretty advanced mechanics courses (as doing physics in rotating coordinate systems is a beast).

Regardless, there's no reason to say that the spin-1 mediated interactions are forces, while the spin-2 mediated interactions (gravity) are not.

 

[James Alton]

An overly-simplified way of stating it is that the field updates at speed c, as gravity waves propagate the changes through the field.

The more complicated way of saying this is that some apparent changes to the field don't need any updates, and so appear to propagate instantaneously. To see how this might work, consider linear motion. With regard to linear motion, simple consistency requires that if we want the gravitational field of a black hole moving linearly, that field must be identical to the field we get from simply taking the black hole's space-time, and transforming to coordinates that are moving with respect to the black hole. This requirement ensures that an object near a moving black hole will be pulled towards the center of the black hole, not towards the position it was 7 minutes ago if the black hole is 7 light minutes away.

It turns out that when you work through the math, gravity not only doesn't need to update for linear motion, but it also doesn't need to update the field for acceleration.

Changes in acceleration, however, need to update, and an object which is changing its acceleration will radiate gravity waves (though typically very, very little unless the change in acceleration is massive, such as for an object very close to a neutron star or black hole).

Thanks for the detailed explanation, that does help a lot!
The discussion of black holes has however generated a new question that I am hoping that someone can help me with. As I understand things, matter being drawn into a black hole from our perspective slows as it approaches the event horizon and if we could see the matter once it reached the EH it would appear frozen ( motion would appear to cease) due to the extreme time dilation. I envision that if we could cut a slice through a black hole and examine it, that we should not see any obvious motion below the EH for the same reason though I understand that we may never know for sure. I don't have a problem with this part but what I don't understand is how the mass located behind an EH can effectively be frozen in it's collapse and yet be free to move through the Universe in every other sense? How is movement of matter towards the center of a black hole any different than this same matter moving through space? James

 

[PeterDonis]

As I understand things, matter being drawn into a black hole from our perspective slows as it approaches the event horizon and if we could see the matter once it reached the EH it would appear frozen ( motion would appear to cease) due to the extreme time dilation.

Your understanding is not correct. You are confusing an effect of the spacetime curvature of a black hole on light rays emitted outward by infalling objects, with an effect on those objects themselves. Infalling objects appear to slow down because of the way the spacetime curvature of the hole affects the light rays those objects emit. But someone falling along with the objects would not see them slow down; everything would look perfectly normal.

f we could cut a slice through a black hole and examine it

We can't. A black hole is not an ordinary object, and it is not correct to think of the region inside the horizon as similar to the region inside the surface of a planet or star. The interior of a black hole is very different.

 

[Chalnoth]

Thanks for the detailed explanation, that does help a lot!
The discussion of black holes has however generated a new question that I am hoping that someone can help me with. As I understand things, matter being drawn into a black hole from our perspective slows as it approaches the event horizon and if we could see the matter once it reached the EH it would appear frozen ( motion would appear to cease) due to the extreme time dilation. I envision that if we could cut a slice through a black hole and examine it, that we should not see any obvious motion below the EH for the same reason though I understand that we may never know for sure. I don't have a problem with this part but what I don't understand is how the mass located behind an EH can effectively be frozen in it's collapse and yet be free to move through the Universe in every other sense? How is movement of matter towards the center of a black hole any different than this same matter moving through space? James

I have imagined along similar lines. It's certainly the case that this doesn't happen with straight general relativity, or even with general relativity with hawking radiation added. In both cases the matter entering the event horizon reaches the singularity in finite time.

But if the horizon is only an apparent horizon, then it is conceivable. In this case, the black hole might be thought of as a sort of massively time-dilated collision, with matter going in and hawking radiation coming out. The ingoing matter gets highly randomized in this situation due to the extreme nature of the spacetime in the black hole.

 

[PeterDonis]

if the horizon is only an apparent horizon, then it is conceivable.

I assume you are referring here to various speculative quantum models, where quantum effects prevent an actual event horizon or singularity from forming, and instead the collapsing matter gets converted to outgoing radiation. In these models, there is indeed only an apparent horizon--that is, a surface at which, locally, outgoing light does not move outward, but stays at the same radius. From the viewpoint of a distant observer, objects falling through this apparent horizon will indeed look similar to objects falling through the event horizon of a Schwarzschild black hole; their light will be redshifted and they will appear to slow down. However, again similarly to the case of the Schwarzschild black hole, an observer falling inward with the object will not see any slowdown; his clock will tick perfectly normally, and he will see objects around him behaving normally. Only when the infalling observer reaches the region inside the apparent horizon where quantum effects become strong will anything different happen to him--and at that point, what happens is not that he sees time slowing down, but that he gets destroyed and converted into Hawking radiation.

 

[James Alton]

I have imagined along similar lines. It's certainly the case that this doesn't happen with straight general relativity, or even with general relativity with hawking radiation added. In both cases the matter entering the event horizon reaches the singularity in finite time.

But if the horizon is only an apparent horizon, then it is conceivable. In this case, the black hole might be thought of as a sort of massively time-dilated collision, with matter going in and hawking radiation coming out. The ingoing matter gets highly randomized in this situation due to the extreme nature of the spacetime in the black hole.

"In both cases the matter entering the event horizon reaches the singularity in finite time" Thanks so much for this insight! I have read in a number of places that time inside of a black hole actually stops and it never made sense to me…this really helps me a LOT. Does time dilation ever reach a maximum value with increasing gravity or does the curve just keep flattening? I have this weird feeling that the shape of the curve is going to resemble the increasing energy required to accelerate mass to velocities approaching c but I am just guessing... It would be wonderful to see a graph or some data that was easy to understand to help me get a better grasp of how to compare different time frames. (hopefully I said that correctly, if not please let me know)

Would it be correct to say that the matter falling into a black hole approaches c within it's time frame reference? If so then can we say that it is the speed limit of c combined with the extreme time dilation that is responsible for the apparent freezing of matter at the event horizon? Absolutely fascinating discussion, thanks again! James

 

[PeterDonis]

Does time dilation ever reach a maximum value with increasing gravity or does the curve just keep flattening?

"Gravitational time dilation" is only a meaningful concept outside the horizon. At or inside the horizon, there are no static observers--i.e., no observers who stay at the same point in space for all time--and gravitational time dilation is defined relative to those observers; it's the difference between the clock rate of a static observer at some finite altitude and the clock rate of a static observer at infinity.

Would it be correct to say that the matter falling into a black hole approaches c within it's time frame reference?

No. Any object (more precisely, any object with nonzero rest mass) is always at rest in its own frame of reference. What happens as an observer falls into a black hole is that, as he passes static observers closer and closer to the horizon, they are moving closer and closer to $c$ relative to him. And when he actually passes the horizon, it is moving at $c$ relative to him.

 

[James Alton]

Your understanding is not correct. You are confusing an effect of the spacetime curvature of a black hole on light rays emitted outward by infalling objects, with an effect on those objects themselves. Infalling objects appear to slow down because of the way the spacetime curvature of the hole affects the light rays those objects emit. But someone falling along with the objects would not see them slow down; everything would look perfectly normal.

"Your understanding is not correct" That is certainly possible! I do accept the fact that from the reference of frame of someone falling into a black hole that the passage of time should look perfectly normal. I am still confused about why matter falling into a black hole is slowed from our distant perspective while that same matter can move through space in a way that looks normal to us.We can't. A black hole is not an ordinary object, and it is not correct to think of the region inside the horizon as similar to the region inside the surface of a planet or star. The interior of a black hole is very different.

I did not realize that I implied any similarities between a black hole and the inside of a planet or star, sorry for any confusion as that was not my intent. I have been told by a number of different sources that time inside of a black hole stops and as such the analogy of taking a (frozen) slice and examining the apparent lack of movement seemed helpful at the time. Thanks for your input. James

 

[PeterDonis]

I have been told by a number of different sources that time inside of a black hole stops

As you should realize by now, those sources are wrong.

 

[PeterDonis]

can we say that it is the speed limit of c combined with the extreme time dilation that is responsible for the apparent freezing of matter at the event horizon?

No. The apparent "freezing" of matter as it approaches the horizon is because of the effect on outgoing light rays of the gravity of the black hole; those light rays are extremely redshifted and slowed down as they climb out to the observer very far away.

 

[James Alton]

No. The apparent "freezing" of matter as it approaches the horizon is because of the effect on outgoing light rays of the gravity of the black hole; those light rays are extremely redshifted and slowed down as they climb out to the observer very far away.

I meant this in the literal sense rather than as would be seen from an observer but I should have been more clear. James

 

[James Alton]

As you should realize by now, those sources are wrong.

Well, I think that what I am learning the most about is to not take to many definite personal positions and to keep asking questions! (grin) But yes, the idea of time actually stopping at the EH or inside of a black hole never made sense to me and I certainly appreciate the information I am getting here. James

 

[PeterDonis]

I meant this in the literal sense rather than as would be seen from an observer

And just to be clear, in the "literal sense", meaning, I assume, what the infalling observer actually experiences, there is no slowing down of time.

 

[James Alton]

And just to be clear, in the "literal sense", meaning, I assume, what the infalling observer actually experiences, there is no slowing down of time.

No, for the purpose of my question I was hoping to eliminate the observational complications to the problem and just discuss what would be actually physically happening and tie it to our distant perspective. Yes, I do realize that this would probably be impossible to do. Assuming that time continues to progress rather than stopping at the EH as some sources indicate to be the case, your explanation of the passage of time for an observer falling into a black hole makes sense to me. Thanks for all of your helpful input. James

 

[James Alton]

No. The apparent "freezing" of matter as it approaches the horizon is because of the effect on outgoing light rays of the gravity of the black hole; those light rays are extremely redshifted and slowed down as they climb out to the observer very far away.

Yes, from an observational perspective this does sound correct to me. What interests me more however is what is actually physically happening rather than just what could be observed. Thanks, James

 

[PeterDonis]

for the purpose of my question I was hoping to eliminate the observational complications to the problem and just discuss what would be actually physically happening and tie it to our distant perspective.

What is actually physically happening is easy: as I said, the infalling observer sees no slowdown of time; everything around him happens normally. But there is no way to "tie it to our distant perspective" that does not involve a choice of convention. There simply is no invariant fact of the matter about how the "distant perspective" is related to what is happening locally to the infalling observer.

 

[Chalnoth]

Would it be correct to say that the matter falling into a black hole approaches c within it's time frame reference?

No. No matter is ever moving at all in its own reference frame. And no matter will ever outrun a light ray.

 

[AgentSmith]

It's usually the other way around. In basic classes, people usually talk about centripetal forces, which are so-called "real" forces. The centrifugal force is usually not dealt with until you get to pretty advanced mechanics courses (as doing physics in rotating coordinate systems is a beast).

Regardless, there's no reason to say that the spin-1 mediated interactions are forces, while the spin-2 mediated interactions (gravity) are not.

That's what I said. In intro courses centrifugal forces are talked about like real forces, and in more advanced course they are called pseudo- or fictitious courses, then we all revert to using centrifugal force, or coriolis force or whatever. We tend to use abbreviated language for convenience. I would hate to see meteorologists using non-inertial reference frames in calculating coriolis forces at different latitudes. As you say, it would be a beast.

Regarding gravity, all that can be said is that Einstein showed gravity not be a Newtonian central force but a property of spacetime when mass is present. The spin-2 mediator for gravity, the graviton, is still hypothetical. If it is ever discovered, then I'll come back and retract everything.

 

[Chalnoth]

That's what I said. In intro courses centrifugal forces are talked about like real forces,

I said centripetal. A centripetal force is a force that keeps an object moving in a circular path, and is opposite and equal to the centrifugal force that is seen in the rotated reference frame. The centripetal force is considered a real force, while the centrifugal force is considered fictitious.

Most introductory physics classes take great care to talk only about the centripetal force.

 

[AgentSmith]

I said centripetal. A centripetal force is a force that keeps an object moving in a circular path, and is opposite and equal to the centrifugal force that is seen in the rotated reference frame. The centripetal force is considered a real force, while the centrifugal force is considered fictitious.

Most introductory physics classes take great care to talk only about the centripetal force.

Sorry. Mea culpa et cetera.