Apparent Speed of Light is a Constant
Everyone knows the measured speed of light is a constant.
We also know that clocks slow down and dimensions shrink
as we approach a mass. If this time slow down and dimension
shrinkage is in proportion, then we would always observe the
same speed of light even if it were not constant. What we are
observing is that the apparent speed of light is a constant. Our
experiments have not actually calculated the absolute speed of
light. A variable speed of light would cause the gravity force,
which we do observe. Therefore, it is most likely that the
speed of light is variable and causes the gravity force.

Here is a nice reference about gravity bending light.
Derivations showing the effects of allowing a variable speed of light.
Restricting gravity to positive potentials can explain the Pioneer 10 anomaly.
Exotic explanation for pioneer anomaly ruled out.