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In [[mathematical physics]], '''vanishing scalar invariant (VSI) spacetimes''' are [[Lorentzian manifold]]s within which all polynomial [[curvature invariant]]s of all orders are vanishing. Although the only [[Riemannian manifold]] with the 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<ref>{{citation|first1=Don N.|last1=Page|title=Nonvanishing Local Scalar Invariants even in VSI Spacetimes with all Polynomial Curvature Scalar Invariants Vanishing|journal=Classical and Quantum Gravity|volume=26|page=055016|year=2009|issue=5|arxiv=0806.2144|doi=10.1088/0264-9381/26/5/055016|bibcode=2009CQGra..26e5016P|s2cid=118331266}}</ref> or carrying out the full [[Cartan–Karlhede algorithm]] on non-scalar quantities.<ref>{{citation|first1=A.|last1=Koutras|title=A spacetime for which the Karlhede invariant classification requires the fourth covariant derivative of the Riemann tensor|journal=Classical and Quantum Gravity|volume=9|page=L143|year=1992|issue=10|doi=10.1088/0264-9381/9/10/003|bibcode=1992CQGra...9L.143K|s2cid=250904726 }}</ref><ref>{{citation|first1=A.|last1=Koutras|first2=C.|last2=McIntosh|title=A metric with no symmetries or invariants|journal=Classical and Quantum Gravity|volume=13|page=L47|year=1996|issue=5|doi=10.1088/0264-9381/13/5/002|bibcode=1996CQGra..13L..47K|s2cid=250905968 }}</ref>
All VSI spacetimes are a subset of [[Kundt spacetime]]s.<ref>{{citation|first1=V.|last1=Pravda|first2=A.|last2=Pravdova|first3=A.|last3=Coley|first4=R.|last4=Milson|title=All spacetimes with vanishing curvature invariants|journal=Classical and Quantum Gravity|volume=19|year=2002|arxiv=gr-qc/0209024|doi=10.1088/0264-9381/19/23/318|issue=23|pages=6213–6236|bibcode=2002CQGra..19.6213P|s2cid=11958495}}</ref> An example withof thisa propertyVSI spacetime in four dimensions is a [[pp-wave spacetime|pp-wave]]. However, VSI spacetimes however also contain some other four-dimensional Kundt spacetimes of [[Petrov type]] N and III. VSI spacetimes in higher dimensions have similar properties as into the four-dimensional case.<ref>{{citation|first1=A.|last1=Coley|first2=R.|last2=Milson|first3=V.|last3=Pravda|first4=A.|last4=Pravdova|title=Vanishing Scalar Invariant Spacetimes in Higher Dimensions|journal=Classical and Quantum Gravity|volume=21|year=2004|issue=23|pages=5519–5542|arxiv=gr-qc/0410070|doi=10.1088/0264-9381/21/23/014|bibcode=2004CQGra..21.5519C|s2cid=17036677}}.</ref><ref>{{citation|first1=A.|last1=Coley|first2=A.|last2=Fuster|first3=S.|last3=Hervik|first4=N.|last4=Pelavas|title=Higher dimensional VSI spacetimes|journal=Classical and Quantum Gravity|volume=23|year=2006|issue=24|pages=7431–7444|arxiv=gr-qc/0611019|doi=10.1088/0264-9381/23/24/014|bibcode=2006CQGra..23.7431C|s2cid=85442360}}</ref>
