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

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Discussion Overview

The discussion revolves around the implications of the Einstein field equations in the context of expanding space and the existence of gravitational fields. Participants explore theoretical aspects of general relativity, particularly concerning scenarios where space may be expanding faster than light and the nature of spacetime in the absence of mass-energy.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that if space is expanding faster than light, there could be regions without gravitational fields, as gravity also travels at the speed of light.
  • Others argue that the expansion of space is often misunderstood and that the big bang did not occur at a specific location but throughout all of space.
  • It is suggested that in the absence of a gravitational field, spacetime can be described as Minkowski spacetime, although this claim is contested.
  • Some participants clarify that the Einstein field equations predict curvature rather than gravitational fields, emphasizing that the concept of a gravitational field is less useful in general relativity.
  • A later reply challenges the notion that spacetime without mass-energy must be Minkowski, introducing the idea of a Milne universe as a non-inertial coordinate system that can arise in such contexts.
  • Participants note that in FLRW spacetimes, the gravitational field is measured as zero by comoving observers, which is attributed to the isotropic nature of the spacetime.
  • There is a suggestion that the original poster's question may not be about measured gravitational fields but rather about the implications of having no mass-energy in the universe.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between gravitational fields and spacetime geometry, with no consensus reached on whether spacetime without mass-energy must be Minkowski. The discussion remains unresolved regarding the implications of expanding space and gravitational fields.

Contextual Notes

Some limitations in the discussion include assumptions about the nature of expansion, the definitions of gravitational fields, and the implications of different cosmological models, which remain unresolved.

zeromodz
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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?
 
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zeromodz said:
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.

zeromodz said:
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.
 
zeromodz said:
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.

zeromodz said:
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.
 
Passionflower said:
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.
 
bcrowell said:
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.
 
Last edited:
Passionflower said:
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.
 
bcrowell said:
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.
 
Passionflower said:
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.

Passionflower said:
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.
 

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