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Geroch 1968 touches on the Kundt type I and II curvature invariants. If I'm understanding correctly, then type I means curvature polynomials. Type II appears to be something else that I confess I don't understand very well. (I happen to own a copy of the book in which the Kundt paper appeared. I looked at the paper, and I can't make heads or tails of it.) Geroch says, "For example, in the plane wave solutions all the type I invariants vanish, yet the Riemann tensor is not zero."
This seems very surprising to me. Am I understanding correctly that all curvature polynomials vanish in the case of a plane wave solution? Why would this be?
Geroch, "What is a singularity in general relativity?," Ann Phys 48 (1968) 526
This seems very surprising to me. Am I understanding correctly that all curvature polynomials vanish in the case of a plane wave solution? Why would this be?
Geroch, "What is a singularity in general relativity?," Ann Phys 48 (1968) 526