Speed of light vertical and horizontal in gravity

Zman
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The speed of light in a gravitational field is predicted to vary between the horizontal and the vertical.
This prediction comes from the Schwarzschild solution.

The vertical speed c = cof
The horizontal speed c = coSQRT(f)

Where f is 1-2GM/rc2
Because f is smaller than 1, the vertical speed of light is less than the horizontal speed.
Presumably the vertical speed can be down or up which means that it is independent of the direction of gravity as long as it is parallel with the gravity.

Has there been an experiment to test for this prediction?

Is this just an issue of coordinate speed?
It is universally agreed that the speed of light measured locally is independent of direction and always give c.
 
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Is this just an issue of coordinate speed?
Yes.
The measurable speed of light is to first order independent of direction even in a gravitational field.
 

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