86 research outputs found
A spacetime not characterised by its invariants is of aligned type II
By using invariant theory we show that a (higher-dimensional) Lorentzian
metric that is not characterised by its invariants must be of aligned type II;
i.e., there exists a frame such that all the curvature tensors are
simultaneously of type II. This implies, using the boost-weight decomposition,
that for such a metric there exists a frame such that all positive boost-weight
components are zero. Indeed, we show a more general result, namely that any set
of tensors which is not characterised by its invariants, must be of aligned
type II. This result enables us to prove a number of related results, among
them the algebraic VSI conjecture.Comment: 14pages, CQG to appea
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
All metrics have curvature tensors characterised by its invariants as a limit: the \epsilon-property
We prove a generalisation of the -property, namely that for any
dimension and signature, a metric which is not characterised by its polynomial
scalar curvature invariants, there is a frame such that the components of the
curvature tensors can be arbitrary close to a certain "background". This
"background" is defined by its curvature tensors: it is characterised by its
curvature tensors and has the same polynomial curvature invariants as the
original metric.Comment: 6 page
Tilted two-fluid Bianchi type I models
In this paper we investigate expanding Bianchi type I models with two tilted
fluids with the same linear equation of state, characterized by the equation of
state parameter w. Individually the fluids have non-zero energy fluxes w.r.t.
the symmetry surfaces, but these cancel each other because of the Codazzi
constraint. We prove that when w=0 the model isotropizes to the future. Using
numerical simulations and a linear analysis we also find the asymptotic states
of models with w>0. We find that future isotropization occurs if and only if . The results are compared to similar models investigated previously
where the two fluids have different equation of state parameters.Comment: 14 pages, 3 figure
Higher dimensional bivectors and classification of the Weyl operator
We develop the bivector formalism in higher dimensional Lorentzian
spacetimes. We define the Weyl bivector operator in a manner consistent with
its boost-weight decomposition. We then algebraically classify the Weyl tensor,
which gives rise to a refinement in dimensions higher than four of the usual
alignment (boost-weight) classification, in terms of the irreducible
representations of the spins. We are consequently able to define a number of
new algebraically special cases. In particular, the classification in five
dimensions is discussed in some detail. In addition, utilizing the (refined)
algebraic classification, we are able to prove some interesting results when
the Weyl tensor has (additional) symmetries.Comment: 25 pages; v2: some notation changed, typos fixed; CQG accepte
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
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