In mathematical physics, vanishing scalar invariant (VSI) spacetimes are Lorentzian manifolds with all polynomial curvature invariants of all orders vanishing.
Although the only Riemannian manifold with VSI property is flat space, the Lorentzian case admits nontrivial spacetimes with this property.
Distinguishing these VSI spacetimes from Minkowski spacetime requires comparing non-polynomial invariants[1] or carrying out the full Cartan–Karlhede algorithm on non-scalar quantities.
VSI spacetimes in higher dimensions have similar properties as in the four-dimensional case.
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