On Friday, November 17, 2017 at 2:27:13 AM UTC-5, stargene wrote:
An impossible question?

I would like to know if there is a straightforward way of calculating
the sum of two different gravitational potentials U and V at some point
x.

To simplify as much as possible, I imagine, say, that two neutron stars
n1 and n2 are in circular orbit around their mutual center of gravity
(*) and that the point x is always outside their orbit but on a line
joining their centers...Something roughly like:

x _ _ _ _ _ _(n1) _ _ _(*) _ _ _(n2)

and r1 is distance between x and n1; r2 is the distance between x and n2.=


Separately and classically, U, for n1 might be:
U = -G M(n1)/r1 and V, for n2 might be: V = -GM(n2)/r2 . But
what would GR say about this?

So, assuming that r1 and r2 are easy to define, would the sum U+V be
analogous to SR's addition of velocities:

w=(u+v)/(1+uv) ,

..where U=-u^2 , V=-v^2 and their sum W = -w^2 ?

Or am I wildly off base? I just realized an added wrinkle he n1 and
n2 are possibly in relativistic motion and my `straight line' thinking
might be naive.

Thanks

Ouch , you have a way of taxing the noodle. To be clear if (*) were
a light then X would never see (*) light as (n1) would always cast
a shadow hiding it from , X , view. You did say

quote

point x is always outside their orbit but on a line
joining their centers...Something roughly like:

end quote.

If N1 mass were a hint less than N2 to compensate for X then I could
see this as a stable orbit for a few months where N1 will always
shade the light of (*) from X position. Assuming these conditions
are met then special relativity could be ignored at these slow
speeds leaving general relativity. GR tracks Newtonian physics of
M * M / r^2 for force or GR shape of space depending on ones preferred
cup of poison. Keep in mind there are few options if a given math
model is used. What happens in real life is where the real beef is.
I will venture a guess that you were thinking in terms of gravitational
shading to see if it would come out in GR. If this was the case
then no it will not to the best of my understanding. Then again
this is a math simulation not real life.