Is there always the same amount of spacetime curvature in the uni.?

[49ers2013Champ]

Is there always the same "amount" of spacetime curvature in the uni.?

Universe is what I meant by uni.

Okay, if matter and energy cannot be created or destroyed, and since they are what causes spacetime to curve, does that mean there will always be the same amount of spacetime curvature occurring in the universe?

I understand that large marterial bodies curve spacetime more than the small ones, but regardless of their size or distribution, is there always the same amount of gravity occurring in the universe?

I am sure "amount" is probably not the best word, but I think you will understand what I'm asking.

 

[PeterDonis]

I am sure "amount" is probably not the best word, but I think you will understand what I'm asking.

Not really; more precisely, I'm not sure that what you mean by "amount of spacetime curvature" matches up well with anything in the actual physics. I think the answer to your question is "no", but I also think you should clarify more precisely what you mean by "amount of spacetime curvature". One good way to clarify would be to explain how you would measure it.

 

[WannabeNewton]

I suspect that you actually mean the curvature of the universe itself, at any given instant of time, and not the curvature of the space-time that models the universe's entire temporal history (extending backwards to the big bang of course). The sectional curvature of the universe itself is a constant $k$, and can be either $k = 1,-1,$ or $0$ depending on what model you choose. Current experimental evidence hints towards something close to $k = 0$.

As far as space-time curvature goes, there are various different curvature quantities one can look at. The Ricci scalar curvature of the FRW space-time for example is given by $R = 6(\frac{\ddot{a}}{a} + \frac{\dot{a}^{2}}{a^{2}})$ where $a = a(\tau)$ is the scale factor thus, as you can see, $R$ is a function of the cosmic time $\tau$.

 

[49ers2013Champ]

Yes, Wannabe. That's what I'm asking. Great answer. I'm going to read your answer a few more times to make sure it sinks in.

Peter, wait a minute. Wouldn't you agree that the sun curves spacetime more than "fill in the blank"? That's what I meant by amount. And so I'm saying, if the overall amount of energy and matter in the universe remains constant, regardless of its density or distribution in space, does that mean that there is always the same overall--or cumulative--"amount" of spacetime curvature, or, as Wannabe pointed out, curvature of the universe?

 

[PeterDonis]

Wouldn't you agree that the sun curves spacetime more than "fill in the blank"?

It depends on what fills in the blank. The Sun curves spacetime more than the Moon (for an appropriate definition of "the amount of curvature"--which you still haven't given), but less than the white dwarf Sirius B, for example.

That's what I meant by amount.

As I just noted, you haven't really given any more information here. How would you measure "amount of spacetime curvature"?

if the overall amount of energy and matter in the universe remains constant

If the universe is spatially infinite, which is what our current best-fit model says, then the overall amount of energy and matter in it is also infinite. Are you taking that into account?

regardless of its density or distribution in space, does that mean that there is always the same overall--or cumulative--"amount" of spacetime curvature, or, as Wannabe pointed out, curvature of the universe?

No. Spacetime curvature certainly depends on density.

 

[Naty1]

if matter and energy cannot be created or destroyed, and since they are what causes spacetime to curve, does that mean there will always be the same amount of spacetime curvature occurring in the universe?

Probably not, but that's a guess. In general stuff evolves with time. wannabe gives one example...Physically, some things wethink we know :

intergalactic large scale distances are expanding,
Galaxies continue to form from primordial gases,
Stars continue to be born while others die,
Supernovas come and go,
black holes likely continue to evolve and grow bigger for a long long time,
our observable portion of the universe is expected to eventually be dark,cold,black,
the cosmological constant is interpreted as a fixed vacuum energy density as 'space' ...expands
...etc

on the other hand, nobody knows much yet about dark matter and dark energy...some 95% of matter/energy...

Well you get the idea: lots going on as the universe evolves...

wannabe shows one measure of curvature related to the scale factor, a basic measure of cosmological distance. That scale factor is based on the assumption of an isotropic and homogeneous universe...an FLRW model of the universe...so it remains valid even as the above physical factors I listed evolve...there are other measures of curvature within the EFE and the λCDM cosmological model.

One last thought: Leonard Susskind says of every 10¹⁰ bits of information in the universe, all but one lie within black holes...Do we understand the implications if that is roughly accurate?