116 research outputs found
The type N Karlhede bound is sharp
We present a family of four-dimensional Lorentzian manifolds whose invariant
classification requires the seventh covariant derivative of the curvature
tensor. The spacetimes in questions are null radiation, type N solutions on an
anti-de Sitter background. The large order of the bound is due to the fact that
these spacetimes are properly , i.e., curvature homogeneous of order 2
but non-homogeneous. This means that tetrad components of are constant, and that essential coordinates first appear as
components of . Covariant derivatives of orders 4,5,6 yield one
additional invariant each, and is needed for invariant
classification. Thus, our class proves that the bound of 7 on the order of the
covariant derivative, first established by Karlhede, is sharp. Our finding
corrects an outstanding assertion that invariant classification of
four-dimensional Lorentzian manifolds requires at most .Comment: 7 pages, typos corrected, added citation and acknowledgemen
All conformally flat pure radiation metrics
The complete class of conformally flat, pure radiation metrics is given,
generalising the metric recently given by Wils.Comment: 7 pages, plain Te
Product Service System Innovation in the Smart City
Product service systems (PSS) may usefully form part of the mix of innovations necessary to move society toward more sustainable futures. However, despite such potential, PSS implementation is highly uneven and limited. Drawing on an alternate socio-technical perspective of innovation, this paper provides fresh insights, on among other things the role of context in PSS innovation, to address this issue. Case study research is presented focusing on a use orientated PSS in an urban environment: the Copenhagen city bike scheme. The paper shows that PSS innovation is a situated complex process, shaped by actors and knowledge from other locales. It argues that further research is needed to investigate how actors interests shape PSS innovation. It recommends that institutional spaces should be provided in governance landscapes associated with urban environments to enable legitimate PSS concepts to co-evolve in light of locally articulated sustainability principles and priorities
Interpreting a conformally flat pure radiation space-time
A physical interpretation is presented of the general class of conformally
flat pure radiation metrics that has recently been identified by Edgar and
Ludwig. It is shown that, at least in the weak field limit, successive wave
surfaces can be represented as null (half) hyperplanes rolled around a
two-dimensional null cone. In the impulsive limit, the solution reduces to a
pp-wave whose direction of propagation depends on retarded time. In the general
case, there is a coordinate singularity which corresponds to an envelope of the
wave surfaces. The global structure is discussed and a possible vacuum
extension through the envelope is proposed.Comment: 9 pages, Plain TeX, 2 figures. To appear in Class. Quantum Grav.
Reference adde
Double-Kasner Spacetime: Peculiar Velocities and Cosmic Jets
In dynamic spacetimes in which asymmetric gravitational collapse/expansion is
taking place, the timelike geodesic equation appears to exhibit an interesting
property: Relative to the collapsing configuration, free test particles undergo
gravitational "acceleration" and form a double-jet configuration parallel to
the axis of collapse. We illustrate this aspect of peculiar motion in simple
spatially homogeneous cosmological models such as the Kasner spacetime. To
estimate the effect of spatial inhomogeneities on cosmic jets, timelike
geodesics in the Ricci-flat double-Kasner spacetime are studied in detail.
While spatial inhomogeneities can significantly modify the structure of cosmic
jets, we find that under favorable conditions the double-jet pattern can
initially persist over a finite period of time for sufficiently small
inhomogeneities.Comment: 37 pages, 5 figures; v2: minor typos correcte
Inadequate reporting of research ethics review and informed consent in cluster randomized trials : review of random sample of published trials
Peer reviewedPublisher PD
On the Symmetries of the Edgar-Ludwig Metric
The conformal Killing equations for the most general (non-plane wave)
conformally flat pure radiation field are solved to find the conformal Killing
vectors. As expected fifteen independent conformal Killing vectors exist, but
in general the metric admits no Killing or homothetic vectors. However for
certain special cases a one-dimensional group of homotheties or motions may
exist and in one very special case, overlooked by previous investigators, a
two-dimensional homethety group exists. No higher dimensional groups of motions
or homotheties are admitted by these metrics.Comment: Plain TeX, 7 pages, No figure
Obtaining a class of Type O pure radiation metrics with a cosmological constant, using invariant operators
Using the generalised invariant formalism we derive a class of conformally
flat spacetimes whose Ricci tensor has a pure radiation and a Ricci scalar
component. The method used is a development of the methods used earlier for
pure radiation spacetimes of Petrov types O and N respectively. In this paper
we demonstrate how to handle, in the generalised invariant formalism,
spacetimes with isotropy freedom and rich Killing vector structure. Once the
spacetimes have been constructed, it is straightforward to deduce their
Karlhede classification: the Karlhede algorithm terminates at the fourth
derivative order, and the spacetimes all have one degree of null isotropy and
three, four or five Killing vectors.Comment: 29 page
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