1,736 research outputs found
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
Equivalence of three-dimensional spacetimes
A solution to the equivalence problem in three-dimensional gravity is given
and a practically useful method to obtain a coordinate invariant description of
local geometry is presented. The method is a nontrivial adaptation of Karlhede
invariant classification of spacetimes of general relativity. The local
geometry is completely determined by the curvature tensor and a finite number
of its covariant derivatives in a frame where the components of the metric are
constants. The results are presented in the framework of real two-component
spinors in three-dimensional spacetimes, where the algebraic classifications of
the Ricci and Cotton-York spinors are given and their isotropy groups and
canonical forms are determined. As an application we discuss Goedel-type
spacetimes in three-dimensional General Relativity. The conditions for local
space and time homogeneity are derived and the equivalence of three-dimensional
Goedel-type spacetimes is studied and the results are compared with previous
works on four-dimensional Goedel-type spacetimes.Comment: 13 pages - content changes and corrected typo
Riemann-Cartan Space-times of G\"odel Type
A class of Riemann-Cartan G\"odel-type space-times are examined in the light
of the equivalence problem techniques. The conditions for local space-time
homogeneity are derived, generalizing previous works on Riemannian G\"odel-type
space-times. The equivalence of Riemann-Cartan G\"odel-type space-times of this
class is studied. It is shown that they admit a five-dimensional group of
affine-isometries and are characterized by three essential parameters : identical triads () correspond to locally
equivalent manifolds. The algebraic types of the irreducible parts of the
curvature and torsion tensors are also presented.Comment: 24 pages, LaTeX fil
Segre Types of Symmetric Two-tensors in n-Dimensional Spacetimes
Three propositions about Jordan matrices are proved and applied to
algebraically classify the Ricci tensor in n-dimensional Kaluza-Klein-type
spacetimes. We show that the possible Segre types are [1,1...1], [21...1],
[31\ldots 1], [z\bar{z}1...1] and degeneracies thereof. A set of canonical
forms for the Segre types is obtained in terms of semi-null bases of vectors.Comment: 14 pages, LaTeX, replaced due to a LaTex erro
A Bright Future for Fluorescence Imaging of Fungi in Living Hosts
Funding: The PhD studentship (A.C.) was funded by the National Centre for the Replacement, Refinement and Reduction of Animals in Research (NC3Rs), grant number NC/N002482/1. We would also like to acknowledge the support of the Medical Research Council Centre for Medical Mycology at the University of Aberdeen (MR/N006364/1).Peer reviewedPublisher PD
On limits of spacetimes -- a coordinate-free approach
A coordinate-free approach to limits of spacetimes is developed. The limits
of the Schwarzschild metric as the mass parameter tends to 0 or are
studied, extending previous results. Besides the known Petrov type D and 0
limits, three vacuum plane-wave solutions of Petrov type N are found to be
limits of the Schwarzschild spacetime.Comment: 19 p
On the limits of Brans-Dicke spacetimes: a coordinate-free approach
We investigate the limit of Brans-Dicke spacetimes as the scalar field
coupling constant omega tends to infinity applying a coordinate-free technique.
We obtain the limits of some known exact solutions. It is shown that these
limits may not correspond to similar solutions in the general relativity
theory.Comment: LaTeX, 16 pp, report DF/UFPB/02-9
Limits of the energy-momentum tensor in general relativity
A limiting diagram for the Segre classification of the energy-momentum tensor
is obtained and discussed in connection with a Penrose specialization diagram
for the Segre types. A generalization of the coordinate-free approach to limits
of Paiva et al. to include non-vacuum space-times is made. Geroch's work on
limits of space-times is also extended. The same argument also justifies part
of the procedure for classification of a given spacetime using Cartan scalars.Comment: LaTeX, 21 page
Collimation of a spherical collisionless particles stream in Kerr space-time
We examine the propagation of collisionless particles emitted from a
spherical shell to infinity. The number distribution at infinity, calculated as
a function of the polar angle, exhibits a small deviation from uniformity. The
number of particles moving from the polar region toward the equatorial plane is
slightly larger than that of particles in the opposite direction, for an
emission radius in extreme Kerr space-time. This means that the black
hole spin exerts an anti-collimation effect on the particles stream propagating
along the rotation axis. We also confirm this property in the weak field limit.
The quadrupole moment of the central object produces a force toward the
equatorial plane. For a smaller emission radius , the absorption of
particles into the black hole, the non-uniformity and/or the anisotropy of the
emission distribution become much more important.Comment: 11 pages, 8 figures; accepted for publication in CQ
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