Higher dimensional VSI spacetimes

Abstract

‡Mathematical Institute, Academy of Sciences, ˇ Zitná 25, 115 67 Prague 1, Czech Republic. We investigate Lorentzian spacetimes where all zeroth and first order curvature invariants vanish and discuss how this class differs from the one where all curvature invariants vanish (VSI). We show that for VSI spacetimes all components of the Riemann tensor and its derivatives up to some fixed order can be made arbitrarily small. We discuss this in more detail by way of examples.

Supersymmetry, holonomy and Kundt spacetimes

“…A number of CSI spacetimes are also known to be solutions of supergravity theory when supported by appropriate bosonic fields [25]. It is known that AdS d × S (N −d) (in short AdS × S) is an exact solution of supergravity (and preserves the maximal number of supersymmetries) for certain values of (N,d) and for particular ratios of the radii of curvature of the two space forms.…”

“…There are a number of other CSI spacetimes known to be solutions of supergravity and admit supersymmetries; namely, generalizations of AdS × S and (generalizations of) the chiral null models [27]. The Weyl type III AdS gyraton [28] (which is a CSI spacetime with the same curvature invariants as pure AdS) is a solution of gauged supergravity (the AdS gyraton can be cast in the Kundt form [25]). …”

“…Some explicit examples of CSI supergravity spacetimes were constructed in [25] by generalising a homogeneous Einstein spacetime, (M Hom ,g), of Kundt form to an inhomogeneous spacetime, (M, g), by including arbitrary functions W (0) i (u, x k ), H (1) (u, x k ) and H (0) (u, x k ). In the examples (M Hom ,g) was chosen to be a regular Lorentzian Einstein solvmanifold or the transverse space was chosen to be the Heisenberg group, SL(2, R), or the 2-sphere, S 2 .…”

“…Therefore the supersymmetry properties of VSI type IIB supergravity solutions with a CCNV were studied [22]. Supersymmetry was also studied in the CSI-CCNV subclass of supergravity spacetimes [25].…”

On Kerr-Schild spacetimes in higher dimensions

“…Our analysis, combined with the results of [22] (where all vacuum Kundt type N solutions have been given) shows that in arbitrary n ≥ 4 dimensions…”