What Do the Einstein Field Equations Reveal About Gravity in Expanding Space?

[zeromodz]

If space is expanding faster than light, wouldn't that mean that there are some parts of space where there exists no gravitational field because gravity travels at c also. What do the Einstein field equations say about space without a gravitational field?

 

[Passionflower]

If space is expanding faster than light, wouldn't that mean that there are some parts of space where there exists no gravitational field because gravity travels at c also.

No.

It is useful to be a little more exact about 'expansion of space'

The models we use to show 'expansion of space' assume two important things, the size of the universe is infinite and there is no empty space between matter.

What do the Einstein field equations say about space without a gravitational field?

When there is no gravitational field spacetime is a Minkowski spacetime as in special relativity. One could still 'tinker' it by introducing a non-zero cosmological constant.

 

[bcrowell]

If space is expanding faster than light, wouldn't that mean that there are some parts of space where there exists no gravitational field because gravity travels at c also.

You seem to be imagining that the big bang was an explosion that occurred in a specific location in space. It wasn't. The big bang occurred throughout all of space.

What do the Einstein field equations say about space without a gravitational field?

The Einstein field equations predict curvature, not gravitational fields. The concept of a gravitational field is not very useful in general relativity, because by the equivalence principle the gravitational field is zero at any location for a free-falling observer.

 

[bcrowell]

When there is no gravitational field spacetime is a Minkowski spacetime as in special relativity.

This is incorrect. For example, in an FRW solution, comoving observers everywhere throughout the universe measure gravitational fields that are zero. However, the spacetime is not Minkowski.

Note that the converse is also false. For example, an accelerating observer in Minkowski space detects a nonvanishing gravitational field.

 

[Passionflower]

This is incorrect. For example, in an FRW solution, comoving observers everywhere throughout the universe measure gravitational fields that are zero. However, the spacetime is not Minkowski.

Note that the converse is also false. For example, an accelerating observer in Minkowski space detects a nonvanishing gravitational field.

Seems like you are mixing up coordinate effects.

A FLRW spacetime (without a cosmological constant) with no mass-energy becomes a Milne universe which is a Minkowski spacetime with a non-inertial coordinate system.

 

[bcrowell]

Seems like you are mixing up coordinate effects.

A FLRW spacetime (without a cosmological constant) with no mass-energy becomes a Milne universe which is a Minkowski spacetime with a non-inertial coordinate system.

In any FLRW spacetime, including those with nonvanishing matter, the gravitational field is zero as measured by any comoving observer. (Actually it vanishes for any free-falling observer, of which comoving observers are an example.) This follows by symmetry, since the spacetime is isotropic.

 

[Passionflower]

In any FLRW spacetime, including those with nonvanishing matter, the gravitational field is zero as measured by any comoving observer. (Actually it vanishes for any free-falling observer, of which comoving observers are an example.) This follows by symmetry, since the spacetime is isotropic.

It seems we are talking about two different things here.

Do you disagree that a spacetime with a zero lambda and without mass and energy must be a Minkowski spacetime?

We should ask the poster of the topic what he is asking, I seriously doubt he is asking about measured gravitational fields, I think he is simply asking if there is no mass-energy in the universe what will happen. But of course I could be wrong.

 

[bcrowell]

It seems we are talking about two different things here.

We're not just talking about two different things. You made a mistake in your #2, and I pointed it out.

We should ask the poster of the topic what he is asking[...]

I agree that it would be good to hear from the OP at this point.