The Strong Energy Condition in General Relativity

[Cerenkov]

Hello.

I've recently been reading this paper... https://arxiv.org/pdf/gr-qc/0001099.pdf ...in the hope that I can begin to understand some the role of the energy conditions in General Relativity. But I'm not making much progress and so I've turned to this paper... https://arxiv.org/pdf/1405.0403.pdf

This section makes some sense to me.

The interpretation of the geometric form of the SEC is similar to that of the NEC. According to equation (2.5.1), the geometric form of the SEC requires that timelike geodesic congruences tend to be convergent in sufficiently small neighborhoods of every spacetime point. This implies that congruences of null geodesics at that point are also convergent. Similarly, according to equation (2.5.2), the interpretation of the physical form is that observers following timelike geodesics will see that “gravity” tends locally to be “attractive” in its action on stuff following both timelike and null geodesics.

I understand the above to (very loosely) mean the following.

1. In GR, gravity is always attractive.
2. The SEC requires that gravity should always act in an, 'attractive' manner.
3. The SEC is violated in situations where space-time is being affected by the opposite of gravity's attraction, i.e., when repulsion occurs.

Please understand that these are very tentative ideas and I probably haven't worded this post anywhere near accurately enough to do justice to the matters in question. Therefore, any help given with the accuracy, meaning and understanding of this issue would be greatly appreciated. I'm here to learn and will gladly accept correction and guidance - because I need these things to learn and progress.

Thank you.

Cerenkov.

 

[PeterDonis]

In GR, gravity is always attractive.

Not quite. The correct statement is that if the SEC holds, then gravity is always attractive. In other words, the SEC is a way of formalizing what "attractive gravity" means.

The SEC requires that gravity should always act in an, 'attractive' manner.

A better way of saying it would be that the SEC formalizes what "attractive gravity" means--in other words, in regions of spacetime where the SEC holds, gravity will be attractive.

The SEC is violated in situations where space-time is being affected by the opposite of gravity's attraction, i.e., when repulsion occurs.

Again, a better way of saying it would be that in regions of spacetime where the SEC does not hold, gravity will not be attractive.

It might be helpful to keep in mind that the SEC is not a law of physics. It's just a condition you can check in any spacetime (if you know the stress-energy tensor).

 

[Cerenkov]

Not quite. The correct statement is that if the SEC holds, then gravity is always attractive. In other words, the SEC is a way of formalizing what "attractive gravity" means.

Ok Peter, I think I see that. Thank you.

A better way of saying it would be that the SEC formalizes what "attractive gravity" means--in other words, in regions of spacetime where the SEC holds, gravity will be attractive.

Again, a better way of saying it would be that in regions of spacetime where the SEC does not hold, gravity will not be attractive.

And this is a clear cut line of demarcation? The SEC either holds or is violated? No middle ground?

It might be helpful to keep in mind that the SEC is not a law of physics. It's just a condition you can check in any spacetime (if you know the stress-energy tensor).

Hmmm... Yes. My earlier post does have a kind of 'Law of Physics' spin to it. Thanks for the clarification.

Now, let me see if I've got this anywhere near right. When attempting to describe the very early universe using GR, theorists are obliged to make assumptions about the physical conditions prevailing in those epochs. Necessarily so, because the opacity of the CMBR prevents direct observations. That's understood.

So, a mathematical formalization like the SEC is imposed on the region of space-time (manifold?) by the theoretician? They assume that gravity is always attractive unless something else implies or indicates otherwise?

But what about inflation? We have lines of inferential evidence for it, but unlike dark energy, no direct observations of it. Does this mean that we infer that the SEC is violated during an inflationary phase we cannot observe?

Or has this more to do with the fact that GR is strictly classical and inflation uses semi-classical gravity, with its quantum-mechanical inputs?

Thanks.

Cerenkov.

 

[PeterDonis]

When attempting to describe the very early universe using GR, theorists are obliged to make assumptions about the physical conditions prevailing in those epochs. Necessarily so, because the opacity of the CMBR prevents direct observations. That's understood.

Yes.

a mathematical formalization like the SEC is imposed on the region of space-time (manifold?) by the theoretician? They assume that gravity is always attractive unless something else implies or indicates otherwise?

It's not "imposed" but assumed in order to see what its consequences are. That helps physicists to understand what sorts of evidence to look for to test whether the assumptions are valid or not.

what about inflation? We have lines of inferential evidence for it, but unlike dark energy, no direct observations of it. Does this mean that we infer that the SEC is violated during an inflationary phase we cannot observe?

We don't infer that the SEC is violated; we infer that inflation takes place, and we deduce from that that the SEC must be violated, since if the SEC is not violated inflation cannot take place. Inflation is a form of "gravitational repulsion", so the SEC has to be violated in any region of spacetime in which inflation is happening.

Or has this more to do with the fact that GR is strictly classical and inflation uses semi-classical gravity, with its quantum-mechanical inputs?

Inflation, or more generally accelerating expansion, requires the SEC to be violated even at the purely classical level. No quantum assumptions are needed. The quantum assumptions help to make SEC violation seem more plausible, since it is already known that certain kinds of quantum field configurations violate it.

 

[Cerenkov]

Peter,

Many thanks for your latest help. I'll be digesting it over the next few days. However, another thought has just occurred to me. If gravity is exclusively attractive in GR, then before inflationary theory introduced the concept of gravitational repulsion, how was the expansion of the universe explained?

In an expanding universe something is causing the galaxies and galactic clusters to move apart from each other. Something not related to inflation. Something that surely cannot be related to GR, which is exclusively attractive. Something that was expected to be overcome by the gravitational attraction of the universe's mass, leading to a closed universe. Something that 'pushes' and doesn't 'pull'.

So, from the time Hubble discovered the expansion (1930?) and up until inflation was introduced(1980?), using only GR, how did scientists explain cosmic expansion?

Thanks.

Cerenkov.

 

[PeterDonis]

If gravity is exclusively attractive in GR

It isn't. You keep confusing "GR" in general with particular solutions. There are particular solutions of the Einstein Field Equation in which gravity is always attractive. But there are also solutions of the EFE in which gravity is not always attractive. "GR" includes both kinds of solutions.

In an expanding universe something is causing the galaxies and galactic clusters to move apart from each other.

In an expanding universe, the matter in the universe is moving apart because of the initial impulse it got at the Big Bang. In other words, it's just inertia. In models without a cosmological constant (i.e., only matter and radiation present, no dark energy), gravity is attractive, so the expansion decelerates over time.

Something not related to inflation.

You are confusing two different periods of the universe's evolution. Inflation occurred before the Big Bang; it is one way of explaining why all the matter in the universe had a huge initial impulse of expansion at the Big Bang. Our current expansion including a cosmological constant, which is causing the expansion to accelerate, is many billions of years after the Big Bang.

 

[Cerenkov]

Thank you again, Peter.

I'll take the time to do your latest reply the justice it deserves and then return here.

All the best.

Cerenkov.