- In image BH is black hole
- P1 is portal number one similarly P2,P3,P4
- P1 is linked with P3
- P2 is linked with P4
- r is distance at which portals are revolving around black hole. r is equal for P1 and P2 Now the question is what will happen in between P3 and P4? Can an object be safe enough get advantage of time dilation , between P3 and p4? I haven't thought about distance 'r' (And what happens if black hole's gravity acts on itself and forms wierd loop?)
The equilibrium point between P3 and P4 is unstable. It also is a three body system which is needlessly difficult to model.
Just use a single pair of portals one of which, P1, orbits the black hole and the other, P2, is some distance away and is orbited by your object at the correct distance for your desired gravitic potential. I am not entirely certain if that would be stable either because black holes have some weird things well beyond my competence close to them. But reducing the number of objects can only help.
Since we are already assume gate technology you might want to make them spherical instead of circular. If you connect a spherical gate surrounding the black hole to another the spherical gate surrounding a volume of space. The entire surrounded volume would have a stable and constant gravitic potential, which is what you probably wanted. Constructing the machinery for the gates seems like a pain, but that is what engineers are for, right?