Suppose I have two massive plates of size $l\times h\times w$ mounted parallel to each other with a distance of $d$ and with a mass density of $\rho$. I send a light beam in the middle between them along the length $l$ and in parallel to them.
How long does it take the light beam, in coordinate time, to pass through the empty space between the plates?
I assume the speed between the plates is basically determined by the gravitational field between the plates and how this then determines the speed of light.
Maybe the better question is: what is the metric tensor between the plates and how does it determine the speed of light?
Given the highly regular setup, I would hope that at least for larger $l$ and $w$ there is a nearly homogeneous (read, constant in a plane or all over) metric tensor "near the middle" of the setup.