# As space-time expands between two stars, what happens to the gravitational potential energy seemingly lost as U~1/r => ZERO.?

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!

• In GR, potential energy conservation is not applicable, ahem... at least that's what I was told. physics.stackexchange.com/questions/2597/…
– user146020
Commented Mar 8, 2017 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? Commented Mar 10, 2017 at 4:37
• . 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.
– user146020
Commented Mar 10, 2017 at 5:25
• @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. Commented Mar 10, 2017 at 5:41
• 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. .
– user146020
Commented Mar 10, 2017 at 6:15