: If the mass of a stellar object can be considered to be concentrated at its center then two objects approaching the mass and : moving on parallel courses will move toward each other. Is this a legitimate example of a curved metric? If so how much of GR : could be explained by expansion of this effect to multi body systems and where would it fail? I'm pretty sure this is a stupid : question but I would really appreciate it if someone would lower themselves to my level. Thanks in advance.

By the way. Curvature means relative acceleration as you know. But geodesic deviation refers needs further comment. When it is said that the there is curvature and the geodesics deviate it is meant that both geodesics are either null or non-null.

By definition a uniform gravitational field has no spacetime curvature. This has been discussed in the literature by, most noticibly Rohrlich - Principle of Equivalence, F. Rohrlich, Ann. Phys. 22, 169-191, (1963), page 173

And more recently by Boulware - Radiation from a Uniformly Accelerated Charge, David G. Boulware, Ann. Phys., 124, (1980), page 174

These are two landmark papers.