Is Energy Conserved in General Relativity?

[zaybu]

It seems that energy is conserved only locally. Globally, with the expansion of the universe and Dark energy density being always constant, it means that energy is increasing. Can anyone clarify this?

Thanks.

 

[JaredJames]

Globally, with the expansion of the universe and Dark energy density being always constant, it means that energy is increasing.

Does it really? Why would that be?

 

[John37309]

Does it really? Why would that be?

LOL...that is funny :)

zaybu,
Yes, energy into any closed system will always equal energy out of that closed system.

Until someone actually shows us a jam-jar full of dark energy, you can take it that it won't effect any energy calculations you will have to do in your lifetime.

John.

 

[WannabeNewton]

It is indeed conserved locally. If you are talking in terms of GR (and I assume you are) then global energy conservation is impossible to define in general. It can really only be defined globally in space - times where there are respective global symmetries.

 

[Antiphon]

I'm told by those who know more than I do about it (on these forums) that GR doesn't conserve energy globally. It has something to do with Gauss's law failing in 4-space.

Apparently there is no problem in GR for the universe to manufacture new energy or annihilate energy.

 

[Drakkith]

I'm told by those who know more than I do about it (on these forums) that GR doesn't conserve energy globally. It has something to do with Gauss's law failing in 4-space.

Apparently there is no problem in GR for the universe to manufacture new energy or annihilate energy.

Is this related to how redshifted light could conserve energy?

 

[zaybu]

I'm told by those who know more than I do about it (on these forums) that GR doesn't conserve energy globally. It has something to do with Gauss's law failing in 4-space.

Apparently there is no problem in GR for the universe to manufacture new energy or annihilate energy.

Yes, this is what I'm talking about. According to GR, energy is not conserved. Krauss has said that the sum is zero. I'm not sure to what he's referring. How does gravitational waves fit in that picture?

Thanks

 

[JesseC]

I was under the impression that energy density of the universe is changing, but that total energy is not.

It was the steady state universe theories, no longer supported by scientific consensus, that required the constant creation of energy to maintain a steady state.

 

[zaybu]

Does it really? Why would that be?

Photons with wavelength "L" and energy "E" become photons with wavelength "K.L" and energy "E/K" if the Universe expands by a factor of "K". So the energy of radiation will go down as "1/K".

On the contrary, the energy stored e.g. in the cosmological constant will expand as "K^3". Why? Well, the energy density carried by the cosmological constant is constant during the cosmological evolution - that's why the "cosmological constant" is called a "cosmological constant". ;-) But the volume of space is literally expanding so the total energy is increasing proportionally to the volume.


So the conventional formulae for the energy of objects propagating upon the background geometry explicitly lead to non-conserved quantities and we can see that they're not conserved. Only the dust (with no pressure) would conserve the energy ("E=mc^2") in an expanding Universe but no physical evolution will guarantee that everything stays in the form of "exact dust".

 

[WannabeNewton]

Yes, this is what I'm talking about. According to GR, energy is not conserved. Krauss has said that the sum is zero. I'm not sure to what he's referring. How does gravitational waves fit in that picture?

Thanks

Gr doesn't say that energy is not conserved. It just has no general global conservation laws. Usually only in the case where space - time has time - like killing vectors can one say there is global energy conservation in that space - time. Gravitational Waves carry energy away from a radiating system and one can define the energy flux of a gravitational wave based upon conservation of energy so that there is no net change in energy but again global energy conservation is not concrete in GR .