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As the space-time between two stars grows (the accelerating expansion of the universe) the gravitational potential energy between two stars is reduced as 1/r -> ZERO (r is the distance between stars).

Is the gravitational potential energy conserved in the form of the 'kinetic energy generated' by the expansion of space-time between the stars: or in other words, if at t=0 the stars were not moving relative to one another, at t>0 the stars would appear to an observer to start to move away from one another, implying kinetic energy is imparted on the star by a force (however this apparent relative motion is due to the expansion of space-time and not a typical force acting to accelerate the object to a particular kinetic energy).

Einstein's insight (in my opinion) was that acceleration and gravity are one in the same. So, thinking in a similar way, the forces on gravitating bodies is the same as the space-time expansion between them? This doesn't seem satisfying: analogy fail :(

This is a 'on the way to work' idea I still think might be interesting for someone who knows what they are doing to hash out! ;)

Thanks!

ab initio in silico
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  • In GR, potential energy conservation is not applicable, ahem... at least that's what I was told. http://physics.stackexchange.com/questions/2597/energy-conservation-in-general-relativity –  Mar 08 '17 at 16:51
  • @Countto10 I have a very superficial understanding of GR, but the post you linked seems to blame the global nature of the metric tensor for not allowing a global conserved energy from being defined. What about locally to a local observer? – ab initio in silico Mar 10 '17 at 04:37
  • . I would like to be able to say that on a sufficiently local scale, the fact the metric goes from $g_{\eta \upsilon}$ to $\mu_{\eta \upsilon} $ restores the conservation of energy that we use in classical mechanics, but to be frank with you, someone with more knowledge of GR is required and I apologise for that. –  Mar 10 '17 at 05:25
  • @Countto10 Let's forget conservation for a second then and let me just ask: "As space-time expansion between two stars increases the distance between the stars, does a distant observer (positioned orthogonal to the line connecting the stars) observe the stars accelerating away from one another at a rate proportional to the Hubble constant? Or, does the expansion of space-time between the stars and the observer negate the effect, and to the observer the stars remain stationary? I am starting to think the latter might be true and there is no observer that would witness the stars separating. – ab initio in silico Mar 10 '17 at 05:41
  • Can I qualify this a little. There are two classes of observers. We on Earth purely infer from observations that spatial expansion is occurring (and accelerating), although obviously we don't see it in real time, only through the benefit of being able to observe supernovae as markers, looking back in time. I would agree with you that any observer living long enough to match the rate of expansion of the universe would also be a participant in the process. . –  Mar 10 '17 at 06:15
  • He would be in a position analogous to an observer in a high speed rocket, who theoretically is aware of special relativistic effects, but is physically unable to directly match distances measured on Earth because of length contraction and time dilation, and needs to use Lorentz transformations to reconcile measurements with an observer in a different frame of reference –  Mar 10 '17 at 06:15
  • I think that you now have two, more focused questions to ask, based on your comments above. 1.Is it true, (or at least related) to say that on a sufficiently local scale, the fact the metric goes from $ g_{\η \υ} $ to $ \μ_{\η\υ}$ is what restores the conservation of energy that we use in classical mechanics, and 2. Does the expansion of space-time between the stars and the observer imply, that to an observer with sufficient longevity, the the stars remain stationary, as he will get "stretched", to the same degree as the stellar distance? –  Mar 10 '17 at 06:30
  • @Countto10, I am working my way back to your latest comments. I have found this post that I am working through: http://physics.stackexchange.com/questions/81695/expansion-of-the-universe-conversion-of-gravitational-potential-energy-to-kinet?rq=1 – ab initio in silico Mar 10 '17 at 06:41

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