Time dilation and gravitational constant

[zonde]

I have a question about gravitational constant.
Gravitational constant is dimensionfull constant but say time is is affected by gravitation causing gravitational time dilation. So the definition of second is local.
Does it means that gravitational constant is well defined locally but not globally?
How this is treated in GR?

 

[A.T.]

Gravitational constant is dimensionfull

Not in the http://en.wikipedia.org/wiki/Geometrized_unit_system" , where it is just 1.

constant but say time is is affected by gravitation causing gravitational time dilation. So the definition of second is local. Does it means that gravitational constant is well defined locally but not globally?

If you use a distant clock to measure some physical processes in a gravity well, you will come up with different values for constants, because everything is slowed down.