Hello I searched a lot but I am not sure if I understood correctly the change in the shape of light cone while speeding up. I am aware that the x and ct axis are getting closer to each other like scissors while you speed up as the graph below shows, both symmetricaly approaching the ct=x or v=c line. But I am not sure if there is a corresponding graph that shows the shape of the light cone. I have found the following cases. 1. Stays the same, keeping its shape, its angle (45o), its circularity. 2. Its direction is now parallel to ct' axis, it keeps the circularity, its symmetrical shape is now round ct' axis and not ct, its opening angle closes and equals the angular difference between ct' and ct=x line (light cone boundaries), until it goes zero when v=c. Then the light cone is just a line. Unfortunately most shapes are from black hole cases, but as I recall gravity is the same as acceleration. Here also rises the question how the light cone also changes in constant speed with no acceleration. 3. It keeps its upward direction but it loses its symmetrical shape round ct axis. Maybe the slice of the future that was a circle with center the axis ct, is now an elipse with two centers, ct axis and ct' axis. The rather radical about this light cone is that it overpasses the initial light cone boundaries and goes under the line ct=x (or v=c). This seems to violate GR rules. In this diagram while in the same direction we go below ct=x, in the opposite we keep ct=-x the boundary. 4. It keeps its symmetrical round shape with the same angle but now round ct' axis. Maybe the slice of the future (perpendicular to ct' now) remains a circle but with center the axis ct'. The rather radical also about this light cone is that it overpasses the initial light cone boundaries and goes under the line ct=x (or v=c). This seems to violate GR rules. In this diagram while in the same direction we go below ct=x, in the opposite we don't keep ct=-x as boundary instead we follow the same angle as ct' to old ct. As I said I am aware that all the above graphs are not exactly the same but with the equivalense of gravity and acceleration and the "hypothetical" invariance of lightcone representation they should in a way (if not exactly) agree in principle. I tried to sum up some details in a table. I would appreciate a comment (even short) for each case and if possible for both constant speed and acceleration. Thanks in advance for your time.