Gravitation of moving objects

[johank]

Assuming a flat, static spacetime, what would the effective force between two objects, with mass m1 and m2 respectively, separated by a distance r from one another, both moving in the same direction with relativistic velocity v, be ?

 

[Jonathan Scott]

Assuming a flat, static spacetime, what would the effective force between two objects, with mass m1 and m2 respectively, separated by a distance r from one another, both moving in the same direction with relativistic velocity v, be ?

For that simple case you can just use Special Relativity and use a Lorentz transformation from the force in the rest frame. It's just the same as if the force were due to a spring or similar.