# Overlapping gravitational field of non-black holes formally creating a black hole situation?

This is a follow-up to the answer about time dilation in the middle between two gravitational forces: John Rennie's diagram describes the situation where the question was about the time dilation between two masses.

Important is not the net force, this can be zero, but the total gravitational potential. Time dilation is described in that answer as $$\frac{dt}{dt_0} = \sqrt{1 - \frac{4GM}{c^2r}}$$ where $t_0$ is measured by a clock far away from the masses.

With the Schwarzschild Radius $r_s = 2GM/c^2$, this can be written as $$\frac{dt}{dt_0} = \sqrt{1 - \frac{2r_2}{r}}$$

which gets 0 and then complex valued as $r$ passes the value of $2r_s$ from above. So we can construct a situation where the radius of the masses $M$ is $R$ such that $r_s<R<r<2r_s$:

Can someone explain what happens within the overlapping area with regard to time dilation, the speed of light, curvature? Is this an "empty" black hole? Or is the computation wrong, because the fields are too strong there? What would be the correct way to compute time dilation then?