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Suppose there is an object floating in space which over time begins to fall toward the source of a gravitational field. As it falls, its motion happens to be such that it gets locked in orbit around the source with a greater velocity than it had before it 'began to fall'. So it's gravitational potential has been converted to kinetic energy. According to relativity, this increased speed should increase the gravitational potential of the object (and therefore the object + the original source of the field), correct?

Does this mean that as a result of this, the expansion of the Universe should slow down slightly (because there is now a slightly greater gravitational potential in the Universe)? And if so, would that imply that the conversion from gravitational potential to kinetic energy is in a sense a conversion between the bulk kinetic energy of the expanding Universe and the local kinetic energy of a test mass?

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Energy is not conserved in GR, in the sense that there is no global, tensorial measure of energy that is conserved and can be defined in all spacetimes. See this question: Total energy of the Universe

However, if the system described in your example is sufficiently isolated, then we can describe that region of space as asymptotically flat, and we have various conserved measures of energy such as the ADM energy. This energy remains constant during the process you describe, so there is no effect on the broader cosmos.

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There's a blog post that may be of some interest to you here: http://motls.blogspot.com/2013/11/the-expansion-is-accelerating-due-to.html

Basically, the universe is constantly expanding at an accelerated rate due to "negative pressure". This is better understood with the Second Friedmann Equation:

$\frac{\ddot a}{a} =-\frac{4\pi G}{3} (\rho + 3p)$

The same principles can be applied, I guess, to your problem.

Let me know if you need anything else!

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Gravitational potential of universe can't be defined now because the universe has been expending due to this we can't find the exist value of gravitational potential. As the diameter of universe has being expend,gravitational potential become decrease & the gravity due to sun on all the planet would be decrease, because sun is the centre and all eight planet revolving around it. Sun has the great centrifugal force. According to Einstein diameter of universe given by the equation: $$D_u=\frac{c^2}{g_u}$$ where $D_u$ is diameter of universe, $c$ is the velocity of light and $g_u$ the gravitational potential of universe.

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  • $\begingroup$ Take advantage of the MathJax rendering engine active on the site. MathJax uses a LaTeX math-mode alike input language. $\endgroup$
    – user36790
    Oct 3, 2015 at 9:59
  • $\begingroup$ Welcome to Physics! To extend the above comment, you can read about MathJax at this link. $\endgroup$
    – Kyle Kanos
    Oct 3, 2015 at 11:02

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