speed of light asymptotic in higher gravity?

Now I'm heard talk of theories involving variable
c and/or G with time but here is a perhaps unrelated
old brainstormed clue of mine (I have a few so far which
are at least entertaining and which I will dig out when I 
have time after my geophysics Ph.D. candidacy exam in December):

Once I thought the speed of light was highly asymptotic
near gravity wells and much faster well away from them
but that would be something you might chuckle at.
Also somewhere in my old files I have some speculation
on the shape of the variation of c with gravity
and it may have been something related to inverse
tangent or a function of that, but I will dig it
out later, sooner if anyone asks me, even just for fun.

So basically perhaps I could sit down with my rusty in spots 
knowledge of physics and in fairly short order rule said 
theory out but I have little time to waste right now so figured
I would use the time to put it out for you to shoot down or modify
as you see fit, and the most advanced astronomers
and some cosmologists, of those on newsgroups, are on 
this group.   Now if Johnathan Thornburg was around
and I asked him he would probably quickly say amusing
idea but improbable for various reasons (say hi to
him for me if you know him).

David
http://www.nfld.com/~dalton