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In other words :

Suppose that there is a flat space-time and there is a beam of light travels between two points [tex]A[/tex] and [tex]B[/tex] and the distance between A and B is [tex]d_0[/tex] .

and then we put a large mass in this flat space time and make a curved one , we would find the beam of light has been bent toward the large mass while it is traveling between the same two points [tex]A[/tex] and [tex]B[/tex] which the distance between them is [tex]d[/tex] .

my question is :

"is the distance between the points in the flat space-time [tex]d_0[/tex] differs form the distance between the same two points in the curved-space time [tex]d[/tex] ???"

I appreciate your comments .....