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. The boundary of this region is called the Event Horizon.