gauss law - Does Gravity Depend on Spatial Dimension?

Consider a line containing two point masses, $m$ and $M$. The line is a $1D$ space.

What's the gravitational force between the two masses?

Newton's formula for the gravitational force $F$ between two masses $m$ and $M$ in 3D space is

$$F=\frac{G M m}{r^2}$$

where $G$ is a constant and $r$ is the distance between the two masses.

The $r$ term is good in a $3D$ space, but in general it's $r^{n-1}$ where $n$ is the dimension of the space. So putting $n=1$ for $1D$ space we get

$$r^{1-1}=r^0=1 \Rightarrow F=GMm \, ,$$

Which means $F$ is independent of distance. Gravity has the same strength no matter how far apart the two objects are!

Of course, this calculation uses Newton's theory of gravity. Perhaps General Relativity would give a different result.