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

[Ahmed Nabi]

Hi everyone!
I am new to cosmology and have come across this unbelieving interesting field quite recently ( after reading 'A Brief History of Time' to be honest ). This is my first post in PF.

Hubble first discover that the universe is expanding with non-constant, accelerating velocity. Also according to GR, gravity is caused by curvature of space-time caused by Earth's Mass. My question is, if Earth is (being a part of the expanding universe) expanding with accelerating velocity in a particular direction, where does the counter gravity produced by it goes? For simplicity, if we consider the elevator as Earth we can feel extra 'push' to floor while elevator is going upward. Where does that extra push goes in case of earth?

My question might seem a bit awkward to someone may be but I believe in 'no shame in asking question' principle :)

 

[Orodruin]

Hubble first discover that the universe is expanding with non-constant, accelerating velocity.

Hubble never discovered that the expansion was accelerating. This is a recent discovery.

Also according to GR, gravity is caused by curvature of space-time caused by Earth's Mass.

No, gravity is curvature of space-time created by all energy and momentum content in the Universe.

if Earth is (being a part of the expanding universe) expanding with accelerating velocity in a particular direction

This is a misconception. The Earth is not accelerating in any direction. The expansion of the universe is an expansion rate, which means that distances are getting larger at a speed which is directly proportional to the distance itself. It does not have a direction associated to it.

 

[Bandersnatch]

Hi Ahmed, welcome to PF!

Let me expand on Orodruin's answer.

The first thing I'd tell you, is that cosmology in popular treatments is rife with imprecise language that can easily confuse the reader if he's not especially careful. That is not entirely a fault of the authors/speakers, as this highly abstract and mathematics-heavy field is hard, if not impossible, to describe unambiguously in words of everyday communication that shies away from equations and graphs.

Already I can see a number of misconceptions you've picked up. For example:
It is not correct to say that the universe is expanding at a velocity, be it constant or not. The universe is expanding at a rate. It grows by a certain percentage over time. By analogy, it's equally incorrect to say it's expanding at velocity as it is to say that deposits on a savings account in a bank grow by a certain amount of $ (or whatever) per month - savings grow by some percentage per month. The exact amount varies depending on how much money you've deposited, and how long they had been there, but in all cases the percentage growth rate is the same.
So, in concrete terms, our universe is growing (currently) at about 1/144th of a percent per million years. That's how it should be understood - as a percentage growth, not a velocity (1/144th of a percent per million years is another way of writing the Hubble constant, by the way).

Hubble was first to notice that there is such a rate of growth. He noticed that a galaxy twice as far would recede twice as fast. In the same way as twice as much money in a bank will grow by twice the amount as it otherwise would. The discovery of importance here is not the amount of recession/growth (specific to anyone single galaxy only), but the overall rate of recession that can be deduced from those individual measurements.
The famous observation is represented by this graph:

where the circles are individual galaxies (nebulae, as they were classified back then).
The general trend of velocities increasing the farther away the galaxy is can be observed.

As Orodruin mentioned, the changing rate of growth is a recent (the last two decades) discovery.

Another misconception is that there is any directionality to the expansion. This is a natural conclusion when one imagines the universe as expanding from some concrete centre as if it were a big explosion of the kind we observe on Earth.

The universal expansion is indeed universal - it applies to every distance everywhere equally (same percentage growth rate), and does not have a centre. The big bang is not to be understood as an explosion seeding the empty space with matter, but as an already existing dense state of (possibly infinite) universe undergoing expansion, diluting and cooling. It did not happen at some point in space - it happened and still happens everywhere.

As such, all observers, regardless of where they are, see themselves as stationary, and all (far away) galaxies as receding from them. This is what the often-invoked balloon analogy tries to aid with visualising. If you pick any point on an expanding balloon's surface to be an observer, it'll measure every other point on the balloon as receding from it with velocity increasing with distance.

So, each point in the expanding universe is effectively stationary. As such, there is no associated acceleration imitating gravity, of the kind you'd experience in an elevator.

Finally, gravitationally-bound objects do not expand together with the rest of space, although I don't think you actually meant that (rather, you meant that Earth is a part of the expansion, being carried by it from some central point - which was addressed above).
You need to go beyond the scale of clusters of galaxies to observe the expansion.
This can be in a simplified way understood in terms of the escape velocity - from Hubble's graph (and Hubble Law generally), you can find the recession velocity of points some distance apart. The escape velocity is determined by all the mass contained in the radius equal to that distance. If the recession velocity is lower than the escape velocity thus calculated, the mass within that radius will remain gravitationally bound, and resist the expansion.
As mentioned before, the recession velocity becomes great enough only on large cosmological scales.

There are a lot of good materials to read on the subject available online, with varying level of complexity. One of the best, clearest, layman-oriented explanations of the current views on cosmology comes from a Scientific American article specifically addressing the most common misconceptions arising when first encountering the balloon analogy (but it has a broader appeal than just that). To be found here:
http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf

We can direct you to more sources should you need them. Spending some time browsing the cosmology section of the forum, where similar questions have been often asked and responded to, might be also a good idea.

 

[Chalnoth]

Hi everyone!
I am new to cosmology and have come across this unbelieving interesting field quite recently ( after reading 'A Brief History of Time' to be honest ). This is my first post in PF.

Hubble first discover that the universe is expanding with non-constant, accelerating velocity. Also according to GR, gravity is caused by curvature of space-time caused by Earth's Mass. My question is, if Earth is (being a part of the expanding universe) expanding with accelerating velocity in a particular direction, where does the counter gravity produced by it goes? For simplicity, if we consider the elevator as Earth we can feel extra 'push' to floor while elevator is going upward. Where does that extra push goes in case of earth?

My question might seem a bit awkward to someone may be but I believe in 'no shame in asking question' principle :)

There is no counter "push". The accelerated expansion is caused by gravity. If you are free-falling in a gravitational field, you feel weightless. Think of the astronauts in orbit: they are in a gravitational field, and are accelerating (the circular motion around the Earth requires constant acceleration towards the Earth). But they are weightless. So no matter the impact of dark energy, we could not feel it in the way we feel an elevator starting and stopping.

 

[Ahmed Nabi]

Thank you @Orodruin, @Bandersnatch and @Chalnoth for your replies. I guess I have adopted a lot of misconception at the very start on which I have to work on.

So, each point in the expanding universe is effectively stationary. As such, there is no associated acceleration imitating gravity, of the kind you'd experience in an elevator.

This makes it pretty much clear. Thank you again

 

[phinds]

I recommend the link in my signature as a good starting point for your reading

 

[Chalnoth]

By the way, for the specific way in which the cosmological constant interacts with gravity, here is the Newtonian approximation of the gravitational force on a mass $m$ by a mass $M$:

F = {-GmM \over r^2} + {\Lambda m r \over 3}

So this is a little weird. Here we have an attractive force between any two masses which is proportional to each mass, but also a small outward acceleration that is only proportional to the mass being acted on. What this means, essentially, is that the cosmological constant creates a little repulsive acceleration between any two objects.

Now, the value of this outward push from the cosmological constant is exceedingly tiny until you get to cosmological scales.

For example, the Sun pulls on the Earth with a force of about $10^{22}N$. The little push on the Earth from dark energy between the Sun and the Earth is about $3.5N$.

 

[AgentSmith]

There is no counter "push". The accelerated expansion is caused by gravity. If you are free-falling in a gravitational field, you feel weightless. Think of the astronauts in orbit: they are in a gravitational field, and are accelerating (the circular motion around the Earth requires constant acceleration towards the Earth). But they are weightless. So no matter the impact of dark energy, we could not feel it in the way we feel an elevator starting and stopping.

It is not clear if gravity, or negative gravity, is the cause of the accelerated expansion or not. Brian Schmidt, one of the Noble laureates who used Type 1a supernovae to discover the acceleration contrary to his expectation, is not sure. We probably need new physics to tell.

 

[Chalnoth]

It is not clear if gravity, or negative gravity, is the cause of the accelerated expansion or not. Brian Schmidt, one of the Noble laureates who used Type 1a supernovae to discover the acceleration contrary to his expectation, is not sure. We probably need new physics to tell.

It's gravity. Whether we're talking about the cosmological constant, or dark energy, or some type of modified gravity theory, the accelerated expansion is driven by gravity, as gravity is the only force that operates on very large scales.

 

[stedwards]

It is not clear if gravity, or negative gravity, is the cause of the accelerated expansion or not. Brian Schmidt, one of the Noble laureates who used Type 1a supernovae to discover the acceleration contrary to his expectation, is not sure. We probably need new physics to tell.

Whether you may have misunderstood or not, could you provide a link to what ever it was Brian Schmidt was uncertain about?

 

[AgentSmith]

Whether you may have misunderstood or not, could you provide a link to what ever it was Brian Schmidt was uncertain about?

I do not have a link handy, unfortunately. He and another astrophysicist discussed the reason(s) for the accelerated expansion in an online course on Cosmology. Of course, he discovered or co-discovered dark energy, the reason for the acceleration, but there is disagreement about its nature. Some call it quintessence, but that's playing word games IMO. Let me do some digging around for a link.

 

[AgentSmith]

It's gravity. Whether we're talking about the cosmological constant, or dark energy, or some type of modified gravity theory, the accelerated expansion is driven by gravity, as gravity is the only force that operates on very large scales.

Gravity is not a force.

 

[Chalnoth]

Gravity is not a force.

What is your basis of this assertion?

 

[Rob Benham]

Bertrand Russell had a lot to say about the use of the term. We all know the sun doesn't set, but the expression is fixed forever.

 

[James Alton]

Hi Ahmed, welcome to PF!
Let me expand on Orodruin's answer.

The first thing I'd tell you, is that cosmology in popular treatments is rife with imprecise language that can easily confuse the reader if he's not especially careful. That is not entirely a fault of the authors/speakers, as this highly abstract and mathematics-heavy field is hard, if not impossible, to describe unambiguously in words of everyday communication that shies away from equations and graphs.

Already I can see a number of misconceptions you've picked up. For example:
It is not correct to say that the universe is expanding at a velocity, be it constant or not. The universe is expanding at a rate. It grows by a certain percentage over time. By analogy, it's equally incorrect to say it's expanding at velocity as it is to say that deposits on a savings account in a bank grow by a certain amount of $ (or whatever) per month - savings grow by some percentage per month. The exact amount varies depending on how much money you've deposited, and how long they had been there, but in all cases the percentage growth rate is the same.
So, in concrete terms, our universe is growing (currently) at about 1/144th of a percent per million years. That's how it should be understood - as a percentage growth, not a velocity (1/144th of a percent per million years is another way of writing the Hubble constant, by the way).

Hubble was first to notice that there is such a rate of growth. He noticed that a galaxy twice as far would recede twice as fast. In the same way as twice as much money in a bank will grow by twice the amount as it otherwise would. The discovery of importance here is not the amount of recession/growth (specific to anyone single galaxy only), but the overall rate of recession that can be deduced from those individual measurements.
The famous observation is represented by this graph:

where the circles are individual galaxies (nebulae, as they were classified back then).
The general trend of velocities increasing the farther away the galaxy is can be observed.

As Orodruin mentioned, the changing rate of growth is a recent (the last two decades) discovery.

Another misconception is that there is any directionality to the expansion. This is a natural conclusion when one imagines the universe as expanding from some concrete centre as if it were a big explosion of the kind we observe on Earth.

The universal expansion is indeed universal - it applies to every distance everywhere equally (same percentage growth rate), and does not have a centre. The big bang is not to be understood as an explosion seeding the empty space with matter, but as an already existing dense state of (possibly infinite) universe undergoing expansion, diluting and cooling. It did not happen at some point in space - it happened and still happens everywhere.

As such, all observers, regardless of where they are, see themselves as stationary, and all (far away) galaxies as receding from them. This is what the often-invoked balloon analogy tries to aid with visualising. If you pick any point on an expanding balloon's surface to be an observer, it'll measure every other point on the balloon as receding from it with velocity increasing with distance.

So, each point in the expanding universe is effectively stationary. As such, there is no associated acceleration imitating gravity, of the kind you'd experience in an elevator.

Finally, gravitationally-bound objects do not expand together with the rest of space, although I don't think you actually meant that (rather, you meant that Earth is a part of the expansion, being carried by it from some central point - which was addressed above).
You need to go beyond the scale of clusters of galaxies to observe the expansion.
This can be in a simplified way understood in terms of the escape velocity - from Hubble's graph (and Hubble Law generally), you can find the recession velocity of points some distance apart. The escape velocity is determined by all the mass contained in the radius equal to that distance. If the recession velocity is lower than the escape velocity thus calculated, the mass within that radius will remain gravitationally bound, and resist the expansion.
As mentioned before, the recession velocity becomes great enough only on large cosmological scales.

There are a lot of good materials to read on the subject available online, with varying level of complexity. One of the best, clearest, layman-oriented explanations of the current views on cosmology comes from a Scientific American article specifically addressing the most common misconceptions arising when first encountering the balloon analogy (but it has a broader appeal than just that). To be found here:
http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf

We can direct you to more sources should you need them. Spending some time browsing the cosmology section of the forum, where similar questions have been often asked and responded to, might be also a good idea.

This is a fascinating area of science for me that I hope to learn more about. As I understand things, the current expansion involves the creation of new space between distant objects such that the more space that currently exists, the faster the expansion. By extrapolating this simple fact, it becomes apparent that in the distant future, all of the galaxies that we currently see will eventually be moving away from us at greater than c and in effect disappear from our perspective. This would mean that space beyond our own galaxy could appear to be devoid of matter and black. What will the future astronomers (that lack the past history) derive from this view of the Universe? We seem to live in a particularly interesting period of time in ways. Thanks for all of the insight and please correct any misconceptions that I might have.

James Alton

 

[Chalnoth]

This is a fascinating area of science for me that I hope to learn more about. As I understand things, the current expansion involves the creation of new space between distant objects such that the more space that currently exists, the faster the expansion. By extrapolating this simple fact, it becomes apparent that in the distant future, all of the galaxies that we currently see will eventually be moving away from us at greater than c and in effect disappear from our perspective. This would mean that space beyond our own galaxy could appear to be devoid of matter and black. What will the future astronomers (that lack the past history) derive from this view of the Universe? We seem to live in a particularly interesting period of time in ways. Thanks for all of the insight and please correct any misconceptions that I might have.

James Alton

In practice, the galaxies we can currently see will become more and more redshifted until they're nearly impossible to detect (this will take a *very* long time, possibly longer than life can exist, and certainly longer than the Earth will exist). We will never be able to see the galaxies evolve past the point that they left our horizon, however.

 

[AgentSmith]

What is your basis of this assertion?

Gravity is a distortion in spacetime. Source: GR per Einstein(and many others).

 

[Chalnoth]

Gravity is a distortion in spacetime. Source: GR per Einstein(and many others).

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

 

[Mordred]

It's gravity. Whether we're talking about the cosmological constant, or dark energy, or some type of modified gravity theory, the accelerated expansion is driven by gravity, as gravity is the only force that operates on very large scales.

I'm not sure I agree with this . Cosmology and the EFE, FLRW metric are based upon GR and thermodynamic laws including energy density to pressure correlations. Pressure is force per unit volune

In terms of the EFE, and ideal gas laws the Cosmological constant may be modeled as opposite to gravity, but the EFE correlates the energy density and pressure correlations due to gravity by the stress energy tensor.

Treating the Cosmological constant as a form of force without specifying its pressure characteristics via

w=\frac{\rho}{p}.

The stress energy tensor to pressure and energy density is correlated via

T^{\mu\nu}=(\rho+p)U^{\mu}U^{\nu}+p \eta^{\mu\nu} ( note in Minkowskii)

is misleading.

The equation of state for Lambda is a
W=-1. Cosmology should be treated in terms of the ideal gas law applications of the FLRW.

The equation of state for the cosmological constant is briefly covered here

http://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology)

 

[Chalnoth]

I'm not sure I agree with this . Cosmology and the EFE, FLRW metric are based upon GR and thermodynamic laws including energy density to pressure correlations. Pressure is force per unit volune

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.

 

[Mordred]

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.

sorry even though I understand what your stating, I fully believe that the best way to describe expansion so one can fully appreciate and understand the acceleration equation, the EFE and FLRW metric is to learn the thermodynamic laws applications.

The Lorentz group in lie algebra is SO(3.1). Gravity is treated the same as any other force in its number of degrees of freedom correlations. One cannot or rather should not separate gravity as being special.

Mass being simply resistance to inertia, resistance can develop through numerous forms such as asymptotic freedom.

Although matter itself has near negligible energy density to pressure influence. Gravities influence upon pressure is still described by the equation of my last post.

your descriptive mislead in my reading as a form of anti gravity. I know this wasn't your intent. Your more knowledgeable than that common error.

Universe geometry is as I know your well aware of the universes actual density vs it's calculated critical density. This is a definition prior to the cosmological constant. However it's still useful in terms of our measurements of lightcones.

Confusing or not takes a side step to accuracy.

How can your response correlate to this article?

https://www.google.ca/url?sa=t&source=web&cd=10&ved=0CDcQFjAJ&url=http://www.tapir.caltech.edu/~chirata/ph217/lec01.pdf&rct=j&q=acceleration equation FLRW metric&ei=AGNIVZGNIdXioASR54GYDQ&usg=AFQjCNFZnOq8s24pz-aF5Z1GJcN27__Pzg&sig2=AChYsp57G3wRQKckN76n0g

how the Cosmological constant and GR applies to the ideal gas laws and pressure is detailed in this article.

How do you expect a new poster to correlate and understand how the thermodynamic laws apply to the FLRW metric without including them. Specifically since the acceleration equation directly uses those terms

 

[Mordred]

Think of it this way, you apply pressure and energy density ( which also correlates temperature and volume)

In this post.

I started working through the equations, and I'm pretty sure this doesn't work. I might have made a mistake, but it really looks like there probably isn't an analytical solution. It's not easy to do the math correctly, though, as the special relativistic equations describe a single particle at a time, while the fluid equations describe the behavior of a collection of particles.

What I did was assume an ideal fluid, for which the conservation of stress energy equation is:

\dot{\rho} + 3{\dot{a} \over a}\left(\rho + p\right) = 0

Typically the way this equation is solved is to convert it into a differential equation in terms of a, by using the substitution:

{d\rho \over dt} = {d\rho \over da}{da \over dt}

Using this and simplifying, the equation becomes:

{d\rho \over da} + {3 \over a}\left(\rho + p\right) = 0

For the case where $p = w\rho$ with constant $w$, this is a very easy differential equation to solve. But it doesn't look to be so easy when you make use of the relativistic pressure of an ideal gas, which I believe is given by:

p^2c^2 = {1 \over 3}\left(\rho^2 - \left({N_0 m c^2 \over a^3}\right)^2\right)

Here $N_0$ is the number density of the particles when $a = 1$, $m$ is the mass of the individual particles, $\rho$ is the energy density, and $p$ is the pressure. Perhaps I've made a mistake in translating momentum to pressure, but the prospects do not look good.

why change this line, fermion are detailed via the fermion Dirac statistics, bosons via the Bose Einstein statistics.

all particles ( DM and DE ) not involved have if memory serves correct 96 degress of freedom via the two mentioned equations. ( SO(5)). We will ignore SO(10)MSSM for this thread.[/QUOTE]

 

[Chalnoth]

Think of it this way, you apply pressure and energy density ( which also correlates temperature and volume)

Yes, because pressure and energy density are the sources of the gravitational field.

 

[Mordred]

Yes, because pressure and energy density are the sources of the gravitational field.

Ah I see, essentially were simply discussing two equally applicable descriptives. Fair enough.

 

[James Alton]

Ah I see, essentially were simply discussing two equally applicable descriptives. Fair enough.

May I ask if you have a position concerning the speed of gravity? I realize that it is a pretty difficult thing to test.

Thanks, James

 

[Mordred]

May I ask if you have a position concerning the speed of gravity? I realize that it is a pretty difficult thing to test.

Thanks, James

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

 

[Chalnoth]

May I ask if you have a position concerning the speed of gravity? I realize that it is a pretty difficult thing to test.

Thanks, James

Under General Relativity, the speed of gravity is the same as the speed of light. It's very hard (though not completely impossible) to make sense of a theory of gravity that has a different speed of gravity than light.

 

[James Alton]

Under General Relativity, the speed of gravity is the same as the speed of light. It's very hard (though not completely impossible) to make sense of a theory of gravity that has a different speed of gravity than light.

Hello, Thanks for your answer and also for the additional insight. Do you think that gravity is continuously regenerated, or is it static? I would seem that in the case of two binary black holes that they would need to be able to update their external fields as they interact and I am confused as to how this could happen when their masses are hidden behind an event horizon? Thanks for any additional information or insight on this problem. James

 

[Chalnoth]

Hello, Thanks for your answer and also for the additional insight. Do you think that gravity is continuously regenerated, or is it static? I would seem that in the case of two binary black holes that they would need to be able to update their external fields as they interact and I am confused as to how this could happen when their masses are hidden behind an event horizon? Thanks for any additional information or insight on this problem. James

Continuously regenerated? I don't know what you mean.

 

[PeterDonis]

I would seem that in the case of two binary black holes that they would need to be able to update their external fields as they interact and I am confused as to how this could happen when their masses are hidden behind an event horizon?

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.)

 

[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.