Now, I know some of you really are interested in this, including the person who private messaged me, and while it is a complicated subject, and though I've given a very short rudimentary way for you to envision using them, they can be used in many different ways, such as replacing the acceleration with a Christoffel symbol, but then you need to start introducing the summation indices and from that you'd get the four force of gravity. Though it's not a force, it's just a notation symmetry to the which we think about the wat the force drops off 1/length^2. If you want to know more, here's Susski