Inertial reference frames

[kurious]

I can make a local inertial reference frame in a gravitational field by creating a frame that is small but close to the source of curvature of space-time.
Alternatively I can make a local inertial reference frame by creating a frame that is large but a long distance from the source of curvature of space-time.
If the reference frame has a mass, is there a quantitative relationship in general relativity between the mass/size of the frame and its distance from the source of curvature of space-time?

 

[selfAdjoint]

If the reference frame has a mass, then it IS a source of curvature, and cannot be separated from that.

 

[pmb_phy]

I can make a local inertial reference frame in a gravitational field by creating a frame that is small but close to the source of curvature of space-time.
Alternatively I can make a local inertial reference frame by creating a frame that is large but a long distance from the source of curvature of space-time.
If the reference frame has a mass, is there a quantitative relationship in general relativity between the mass/size of the frame and its distance from the source of curvature of space-time?

Not one that is readily available but if one is ambitious it can be calculated. I'm not that ambitious though. :-)

Pete