Force Vector representing negative curvature -Math/code help

[griffman99h]

I have been searching for a solution to what I thought was a simple idea. I'm hoping I can explain it here well enough to get some traction so I can move forward with my simulation design and coding I'm more familiar with.

I'm trying to construct an n-body simulation of rigid bodies with variable size and mass. Think along the lines of a star/planet gravity game. While there is the normal gravity force of n-body attraction, there is also a vector field with in the space centered on origin point (0,0,0). this force is 0 at origin but increases as you move out. The vector code is simple for single planar forces but for 3 dimensional fields I'm not sure how to code this correctly.

The result cannot be created by a rigid body of 0 size and X mass at point (0,0,0) as the acceleration would be wrong. A closer result could be created by a hollow object of X size with infinite mass at radius R with a negative gravitational constant. But that adds more problems for the more standard n-body interactions within the sphere.

This is suppose to represent spacetime with with negative curvature. The tensor math for spacetime equations is way beyond my abilities and I don't think a 3d engine would handle much past n=10 bodies if at all. Any guidance would be most welcome.