1,757 research outputs found
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
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
SO(n + 1) Symmetric Solutions of the Einstein Equations in Higher Dimensions
A method of solving the Einstein equations with a scalar field is presented.
It is applied to find higher dimensional vacuum metrics invariant under the
group SO(n + 1) acting on n-dimensional spheres.Comment: 11 page
A note on the peeling theorem in higher dimensions
We demonstrate the ``peeling property'' of the Weyl tensor in higher
dimensions in the case of even dimensions (and with some additional
assumptions), thereby providing a first step towards understanding of the
general peeling behaviour of the Weyl tensor, and the asymptotic structure at
null infinity, in higher dimensions.Comment: 5 pages, to appear in Class. Quantum Gra
Death and the Pearl Maiden
Shows how English responses to the Black Death were hidden in plain sight—as seen in the Pearl, Cleanness, Patience, and Sir Gawain and the Green Knight poems
Kundt spacetimes as solutions of topologically massive gravity
We obtain new solutions of topologically massive gravity. We find the general
Kundt solutions, which in three dimensions are spacetimes admitting an
expansion-free null geodesic congruence. The solutions are generically of
algebraic type II, but special cases are types III, N or D. Those of type D are
the known spacelike-squashed AdS_3 solutions, and of type N are the known AdS
pp-waves or new solutions. Those of types II and III are the first known
solutions of these algebraic types. We present explicitly the Kundt solutions
that are CSI spacetimes, for which all scalar polynomial curvature invariants
are constant, whereas for the general case we reduce the field equations to a
series of ordinary differential equations. The CSI solutions of types II and
III are deformations of spacelike-squashed AdS_3 and the round AdS_3,
respectively.Comment: 30 pages. This material has come from splitting v1 of arXiv:0906.3559
into 2 separate papers. v2: minor changes
Observational Constraints on the Averaged Universe
Averaging in general relativity is a complicated operation, due to the
general covariance of the theory and the non-linearity of Einstein's equations.
The latter of these ensures that smoothing spacetime over cosmological scales
does not yield the same result as solving Einstein's equations with a smooth
matter distribution, and that the smooth models we fit to observations need not
be simply related to the actual geometry of spacetime. One specific consequence
of this is a decoupling of the geometrical spatial curvature term in the metric
from the dynamical spatial curvature in the Friedmann equation. Here we
investigate the consequences of this decoupling by fitting to a combination of
HST, CMB, SNIa and BAO data sets. We find that only the geometrical spatial
curvature is tightly constrained, and that our ability to constrain dark energy
dynamics will be severely impaired until we gain a thorough understanding of
the averaging problem in cosmology.Comment: 6 pages, 4 figure
Generalization of the Geroch-Held-Penrose formalism to higher dimensions
Geroch, Held and Penrose invented a formalism for studying spacetimes
admitting one or two preferred null directions. This approach is very useful
for studying algebraically special spacetimes and their perturbations. In the
present paper, the formalism is generalized to higher-dimensional spacetimes.
This new formalism leads to equations that are considerably simpler than those
of the higher-dimensional Newman-Penrose formalism employed previously. The
dynamics of p-form test fields is analyzed using the new formalism and some
results concerning algebraically special p-form fields are proved.Comment: 24 page
Kerr-Schild spacetimes with (A)dS background
General properties of Kerr-Schild spacetimes with (A)dS background in
arbitrary dimension are studied. It is shown that the geodetic Kerr-Schild
vector k is a multiple WAND of the spacetime. Einstein Kerr-Schild spacetimes
with non-expanding k are shown to be of Weyl type N, while the expanding
spacetimes are of type II or D. It is shown that this class of spacetimes obeys
the optical constraint. This allows us to solve Sachs equation, determine
r-dependence of boost weight zero components of the Weyl tensor and discuss
curvature singularities.Comment: 17 pages, minor change
- …