Is a null hyperplane a Cauchy surface in Minkowski spacetime?
What in case of other spacetimes?
This is something that you should try to work through. What is a Cauchy surface? A readable definition is given on pages 79-80 of Sean Carroll's book An Introduction to General Relativity: Spacetime Geometry. This is just one example of where Carroll's book is better than Carroll'a arXiv notes.
I am not sure what you're asking.
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