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Is there a deeper relationship between symmetry and gravitational potential comparing Newton's and Einstein's gravity?
In this question, see Why is general relativity in (2+1) dimensions different from cylindrical systems in (3+1) dimensional GR?, it is mentioned
"The gravitational potential Φ of an infinite rod ...
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Intuition behind gravitational potential
Gravitational potential at a point is equal to work done in bringing a unit mass from infinity to a particular point
That was the text book definition
$$V_{p} = -\frac{GM}{r}$$
If we calculate $V_p$ ...
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Why is the Taylor expansion of the gravitational potential cut off after first term?
In this answer to a question on this site, the gravitational potential of the Earth is expanded as
$$U(r) \approx U(r_0) + \left.\frac {dU(r)}{dr}\right|_{r=r_0}(r-r_0),$$
keeping only the linear term....
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