62 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
Local freedom in the gravitational field revisited
Maartens {\it et al.}\@ gave a covariant characterization, in a 1+3 formalism
based on a perfect fluid's velocity, of the parts of the first derivatives of
the curvature tensor in general relativity which are ``locally free'', i.e. not
pointwise determined by the fluid energy momentum and its derivative. The full
decomposition of independent curvature derivative components given in earlier
work on the spinor approach to the equivalence problem enables analogous
general results to be stated for any order: the independent matter terms can
also be characterized. Explicit relations between the two sets of results are
obtained. The 24 Maartens {\it et al.} locally free data are shown to
correspond to the quantities in the spinor approach, and the
fluid terms are similarly related to the remaining 16 independent quantities in
the first derivatives of the curvature.Comment: LaTeX. 13 pp. To be submitted to Class. Quant. Gra
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
Impact of CONSORT extension for cluster randomised trials on quality of reporting and study methodology : review of random sample of 300 trials, 2000-8
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