Does space time cone live in spacetime manifold or in its tangent space?
Given that it is defined by g(v, v) >= 0 I think it operates on velocity vectors which means space time cone is a structure defined on tangent space at every point.
However wikpedia says "In special and general relativity, a light cone is the path that a flash of light, emanating from a single event (localized to a single point in space and a single moment in time) and traveling in all directions, would take through spacetime."
This would imply the cone is in spacetime (manifold) itself.
I still think cone is defined in tangent space. Is this correct?