No. The frequency of the light just increases as it picks up gravitational potential energy. Similarly if it is 'climbing out' of a gravitational field i twill lose energy and its frequency will decreade and become 'redshifted' as viewed by someone farther outside the well. The 'local' speed stays the same as measured by someone freely-falling into the well and watching the photon pass by. This is the only observer who is in what relativity would consider a 'proper rest frame'.

Return to Dr. Odenwald's Gravity page at the Astronomy Cafe Blog.