We assume that there is an infinite density at the center of a black hole. But we also know that if it was really infinite, it would apply an infinite gravitational force to masses even if they were millions of light years away. So there must be a multivariable calculus equation for a black hole's force field. There must be some boundaries.
However, we also know that some black holes even bend lights, massless particals, so we are also pretty sure somewhere in the equation for some specific conditions there is an infinity. So in the equation, the boundaries must be set by another dimension, another variables we can not observe that are beyond 3 dimensions and space-time compression.
So this is where I got so far. If some variables from another dimension(s) involved, what are they? If not, how a black hole which is assumed to have an infinite density, does not effect us (Earth) infinitely?