Higher dimensional VSI spacetimes and supergravity

We present the explicit form of higher dimensional VSI spacetimes in arbitrary number of dimensions. We discuss briefly the VSI's in the context of supergravity/strings.Comment: 3 pages, to be published in the Proceedings of the Eleventh Marcel Grossmann Meeting on General Relativit

Higher dimensional VSI spacetimes

We present the explicit metric forms for higher dimensional vanishing scalar invariant (VSI) Lorentzian spacetimes. We note that all of the VSI spacetimes belong to the higher dimensional Kundt class. We determine all of the VSI 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. The Ricci type N subclass is related to the chiral null models and includes the relativistic gyratons and the higher dimensional pp-wave spacetimes. The spacetimes under investigation are of particular interest since they are solutions of supergravity or superstring theory.Comment: 14 pages, changes in second paragraph of the discussio

Lorentzian spacetimes with constant curvature invariants in three dimensions

In this paper we study Lorentzian spacetimes for which all polynomial scalar invariants constructed from the Riemann tensor and its covariant derivatives are constant (CSI spacetimes) in three dimensions. We determine all such CSI metrics explicitly, and show that for every CSI with particular constant invariants there is a locally homogeneous spacetime with precisely the same constant invariants. We prove that a three-dimensional CSI spacetime is either (i) locally homogeneous or (ii) it is locally a Kundt spacetime. Moreover, we show that there exists a null frame in which the Riemann (Ricci) tensor and its derivatives are of boost order zero with constant boost weight zero components at each order. Lastly, these spacetimes can be explicitly constructed from locally homogeneous spacetimes and vanishing scalar invariant spacetimes.Comment: 14 pages; Modified to match published versio

Slices of the Kerr ergosurface

The intrinsic geometry of the Kerr ergosurface on constant Boyer-Lindquist (BL), Kerr, and Doran time slices is characterized. Unlike the BL slice, which had been previously studied, the other slices (i) do not have conical singularities at the poles (except the Doran slice in the extremal limit), (ii) have finite polar circumference in the extremal limit, and (iii) for sufficiently large spin parameter fail to be isometrically embeddable as a surface of revolution above some latitude. The Doran slice develops an embeddable polar cap for spin parameters greater than about 0.96.Comment: 13 pages, 6 figures; v.2: minor editing for clarification, references added, typos fixed, version published in Classical and Quantum Gravit

CCNV Space-Times as Potential Supergravity Solutions

It is of interest to study supergravity solutions preserving a non-minimal fraction of supersymmetries. A necessary condition for supersymmetry to be preserved is that the spacetime admits a Killing spinor and hence a null or timelike Killing vector field. Any spacetime admitting a covariantly constant null vector field ($CCNV$) belongs to the Kundt class of metrics, and more importantly admits a null Killing vector field. We investigate the existence of additional non-spacelike isometries in the class of higher-dimensional $CCNV$ Kundt metrics in order to produce potential solutions that preserve some supersymmetries.Comment: 14 page