12 research outputs found
Supergravity solutions with constant scalar invariants
We study a class of constant scalar invariant (CSI) spacetimes, which belong
to the higher-dimensional Kundt class, that are solutions of supergravity. We
review the known CSI supergravity solutions in this class and we explicitly
present a number of new exact CSI supergravity solutions, some of which are
Einstein.Comment: 12 pages; to appear in IJMP
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
Metrics With Vanishing Quantum Corrections
We investigate solutions of the classical Einstein or supergravity equations
that solve any set of quantum corrected Einstein equations in which the
Einstein tensor plus a multiple of the metric is equated to a symmetric
conserved tensor constructed from sums of terms the involving
contractions of the metric and powers of arbitrary covariant derivatives of the
curvature tensor. A classical solution, such as an Einstein metric, is called
{\it universal} if, when evaluated on that Einstein metric, is a
multiple of the metric. A Ricci flat classical solution is called {\it strongly
universal} if, when evaluated on that Ricci flat metric,
vanishes. It is well known that pp-waves in four spacetime dimensions are
strongly universal. We focus attention on a natural generalisation; Einstein
metrics with holonomy in which all scalar invariants are zero
or constant. In four dimensions we demonstrate that the generalised
Ghanam-Thompson metric is weakly universal and that the Goldberg-Kerr metric is
strongly universal; indeed, we show that universality extends to all
4-dimensional Einstein metrics. We also discuss generalizations
to higher dimensions.Comment: 23 page
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
Classification of the Weyl Tensor in Higher Dimensions and Applications
We review the theory of alignment in Lorentzian geometry and apply it to the
algebraic classification of the Weyl tensor in higher dimensions. This
classification reduces to the the well-known Petrov classification of the Weyl
tensor in four dimensions. We discuss the algebraic classification of a number
of known higher dimensional spacetimes. There are many applications of the Weyl
classification scheme, especially in conjunction with the higher dimensional
frame formalism that has been developed in order to generalize the four
dimensional Newman--Penrose formalism. For example, we discuss higher
dimensional generalizations of the Goldberg-Sachs theorem and the Peeling
theorem. We also discuss the higher dimensional Lorentzian spacetimes with
vanishing scalar curvature invariants and constant scalar curvature invariants,
which are of interest since they are solutions of supergravity theory.Comment: Topical Review for Classical and Quantum Gravity. Final published
versio