Research on conservation of spacetime curvature

[Structure seeker]

TL;DR

Is there any research done on conservation of (integrated over all spacetime) spacetime curvature?

After trying to kinda get a picture of the field of play in quantum physics according to the standard model, a question came up. I tried to formulate the known bosons each as a particle transferring some property.

1. Photons transfer electric charge: the electromagnetic force gives attraction between positive and negative charges so an electronic current
2. Gluons transfer color charge
3. The 3 weak bosons transfer weak isospin
4. The Higgs mechanism transfers a combination of weak isospin and weak hypercharge
5. Gravitons, if they exist, transfer spacetime curvature?

The first 4 properties transferred are conserved (by quantum conservation laws). My question is: has any research been done on whether spacetime curvature (integrated over all of it) could be conserved? I'm especially interested in loop quantum gravity views on this matter (hope I can sort of understand that but OK)

The only thing I found on internet is a physics stackexchange question https://physics.stackexchange.com/questions/130379/conservation-in-space-time-curvature where the question is waved away with the observation that the universe at large is not curved, so what curvature? But IMO that might be in fact an indication that every negative curvature induces an equal opposite positive curvature somehow.

 

[PeterDonis]

has any research been done on whether spacetime curvature (integrated over all of it) could be conserved?

"Spacetime curvature" is not even a number; it's a tensor. In GR it is not a conserved quantity.

the question is waved away with the observation that the universe at large is not curved

This answer confuses spacetime curvature with spatial curvature in our best current model of our universe. They're not the same.

 

[Structure seeker]

I'm not a physicist but more a hobbyist in the area of mathematical physics, so whether it matches GR or not is outside my area of expertise.

Regardless, taking the analysis I made seriously could lead to interesting viewpoints or directions to new theories. It's clear this analysis got no critique, so the observations I made are somewhat peer-reviewed now. But no wild speculation here please.

 

[Ibix]

It's clear this analysis got no critique

...apart from Peter pointing out that curvature is a tensor, not a number, which renders questions about a "total curvature" meaningless, even before you get to questions about conservation.

 

[Structure seeker]

Let me just cite V. Retsnoi which can be found as K20-re.pdf in this link: http://www.mathem.pub.ro/proc/bsgp-20/

 

[PeterDonis]

Let me just cite V. Retsnoi which can be found as K20-re.pdf in this link: http://www.mathem.pub.ro/proc/bsgp-20/

This is about integration of tensor fields. It has nothing whatever to do with the speculative claims you make in your OP.

 

[PeterDonis]

It's clear this analysis got no critique, so the observations I made are somewhat peer-reviewed now.

If by this you mean that you think the fact that nobody has given you a detailed refutation implies that we think there is some value in your speculations, you are wrong.

taking the analysis I made seriously could lead to interesting viewpoints or directions to new theories.

That is not what PF is for. PF is not for discussion of personal research or personal speculations. It is to help people understand physics that is already mainstream. If you think there is something useful in the speculations you are making, get a peer-reviewed paper published.

Thread closed.