If you (somehow) keep accelerating in one direction, there are events you will never observe. It's called a Rindler horizon. Your world-line traces a hyperbola.

If you (somehow) keep accelerating in one direction, there are events you will never observe. It's called a Rindler horizon. Your world-line traces a hyperbola... which will always outpace photons from certain spacetime locations. https://youtu.be/7cj6oiFDEXc https://youtu.be/7cj6oiFDEXc