Worldlines represent the histories of objects in spacetime. No mechanical experiment can distinguish a state of absolute rest from uniform straight-line motion. In particular, the speed of light is the same constant, independent of the motion of the source. A uniform arrangement of Light Cones.
Gravity is negligible.
Light travels in straight paths. A non-uniform arrangement of Light Cones. Gravity is important. Light travels in a curved path. The Light Cones are arranged so that there is region of spacetime where all Light Cones tip over and point inward.