Math, again, people!
A couple of posts ago I introduced myself to
geodesics as
free fall trajectories in curved spacetime. The problem with this description -one of them- is it's saying not enough. What I've learned since then about geodesics it's still not enough, but it's a step forward, so better than nothing.
This post was intended to solve geodesic equation for an
easy case and show that spacetime nature depends on 4 coordinates -3 in space and 1 in time. The problem is the answer is not as straightforward as I expected. Let's see it anyway.
A geodesic is a curve. And like any curve, it can be described mathematically. General, index form is:
