Vanishing Scalar Invariant Spacetimes in Higher Dimensions
نویسنده
چکیده
We study manifolds with Lorentzian signature and prove that all scalar curvature invariants of all orders vanish in a higher-dimensional Lorentzian spacetime if and only if there exists an aligned non-expanding, non-twisting, geodesic null direction along which the Riemann tensor has negative boost order.
منابع مشابه
ar X iv : h ep - t h / 07 03 25 6 v 1 2 8 M ar 2 00 7 NIKHEF / 2007 - 008 VANISHING SCALAR INVARIANT SPACETIMES IN SUPERGRAVITY
We show that the higher-dimensional vanishing scalar invariant (VSI) spacetimes with fluxes and dilaton are solutions of type IIB supergravity, and we argue that they are exact solutions in string theory. We also discuss the supersymmetry properties of VSI spacetimes. [PACS: 04.20.Jb, 04.65.+e]
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We present the explicit metric forms for higher dimensional vanishing scalar invariant (V SI) Lorentzian spacetimes. We note that all of the V SI spacetimes belong to the higher dimensional Kundt class. We determine all of the V SI spacetimes which admit a covariantly constant null vector, and we note that in general in higher dimensions these spacetimes are of Ricci type III and Weyl type III....
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