I'm trying to wrap my head around how geodesics describe trajectories at the moment.
I get that for events to be causally connected, they must be connected by a timelike curve, so free objects must move along a timelike geodesic. And a timelike geodesic can be defined as a geodesic that lies within the light cone.
I want to know why exactly null geodesics define the light cone. Or, why null geodesics define the path of light.
Also, if there's a better explanation why matter follows timelike geodesics, that would also be welcome.