Please explain these Equations in GR, Modified Universal law of Gravity.

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Space time Geometry and GR, taken from lecture notes

http://www.mth.kcl.ac.uk/courses/cm334.html [Broken]

http://www.mth.kcl.ac.uk/courses/cm334/Lectures0910.pdf
from pages 3 and 4

Newton's universal law of gravity is getting modified.

it says using the result, from where this result comes from?

Screenshot1.png


and as follows with this page

Screenshot2.png


after equation 4, it says that using the fact that... where this equation is coming from and how can I understand this, can anyone explain please?
 
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atyy
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