4,150 research outputs found
Relativistic Positioning Systems: The Emission Coordinates
This paper introduces some general properties of the gravitational metric and
the natural basis of vectors and covectors in 4-dimensional emission
coordinates. Emission coordinates are a class of space-time coordinates defined
and generated by 4 emitters (satellites) broadcasting their proper time by
means of electromagnetic signals. They are a constitutive ingredient of the
simplest conceivable relativistic positioning systems. Their study is aimed to
develop a theory of these positioning systems, based on the framework and
concepts of general relativity, as opposed to introducing `relativistic
effects' in a classical framework. In particular, we characterize the causal
character of the coordinate vectors, covectors and 2-planes, which are of an
unusual type. We obtain the inequality conditions for the contravariant metric
to be Lorentzian, and the non-trivial and unexpected identities satisfied by
the angles formed by each pair of natural vectors. We also prove that the
metric can be naturally split in such a way that there appear 2 parameters
(scalar functions) dependent exclusively on the trajectory of the emitters,
hence independent of the time broadcast, and 4 parameters, one for each
emitter, scaling linearly with the time broadcast by the corresponding
satellite, hence independent of the others.Comment: 13 pages, 3 figures. Only format changed for a new submission.
Submitted to Class. Quantum Gra
Positioning systems in Minkowski space-time: from emission to inertial coordinates
The coordinate transformation between emission coordinates and inertial
coordinates in Minkowski space-time is obtained for arbitrary configurations of
the emitters. It appears that a positioning system always generates two
different coordinate domains, namely, the front and the back emission
coordinate domains. For both domains, the corresponding covariant expression of
the transformation is explicitly given in terms of the emitter world-lines.
This task requires the notion of orientation of an emitter configuration. The
orientation is shown to be computable from the emission coordinates for the
users of a `central' region of the front emission coordinate domain. Other
space-time regions associated with the emission coordinates are also outlined.Comment: 20 pages; 1 figur
DAMA detection claim is still compatible with all other DM searches
We show that the annual modulation signal observed by DAMA can be reconciled
with all other negative results from dark matter searches with a conventional
halo model for particle masses around 5 to 9 GeV. We also show which particular
dark matter stream could produce the DAMA signal.Comment: Talk given at TAUP2005, Sept. 10-14 2005, Zaragoza (Spain). 3 pages,
4 figure
On the degrees of freedom of a semi-Riemannian metric
A semi-Riemannian metric in a n-manifold has n(n-1)/2 degrees of freedom,
i.e. as many as the number of components of a differential 2-form. We prove
that any semi-Riemannian metric can be obtained as a deformation of a constant
curvature metric, this deformation being parametrized by a 2-for
Rainich theory for type D aligned Einstein-Maxwell solutions
The original Rainich theory for the non-null Einstein-Maxwell solutions
consists of a set of algebraic conditions and the Rainich (differential)
equation. We show here that the subclass of type D aligned solutions can be
characterized just by algebraic restrictions.Comment: 12 pages; v2: appendix with notatio
On the classification of type D spacetimes
We give a classification of the type D spacetimes based on the invariant
differential properties of the Weyl principal structure. Our classification is
established using tensorial invariants of the Weyl tensor and, consequently,
besides its intrinsic nature, it is valid for the whole set of the type D
metrics and it applies on both, vacuum and non-vacuum solutions. We consider
the Cotton-zero type D metrics and we study the classes that are compatible
with this condition. The subfamily of spacetimes with constant argument of the
Weyl eigenvalue is analyzed in more detail by offering a canonical expression
for the metric tensor and by giving a generalization of some results about the
non-existence of purely magnetic solutions. The usefulness of these results is
illustrated in characterizing and classifying a family of Einstein-Maxwell
solutions. Our approach permits us to give intrinsic and explicit conditions
that label every metric, obtaining in this way an operational algorithm to
detect them. In particular a characterization of the Reissner-Nordstr\"{o}m
metric is accomplished.Comment: 29 pages, 0 figure
Extrinsic Ricci Flow on Surfaces of Revolution
An extrinsic representation of a Ricci flow on a differentiable n-manifold M is a family of submanifolds S(t), each smoothly embedded in Rn+k, evolving as a function of time t such that the metrics induced on the submanifolds S(t) by the ambient Euclidean metric yield the Ricci flow on M. When does such a representation exist? We formulate this question precisely and describe a new, comprehensive way of addressing it for surfaces of revolution in R3. Our approach is to build the desired embedded surfaces of revolution S(t) in R3 into the flow at the outset by rewriting the Ricci flow equations in terms of extrinsic geometric quantities in a natural way. This identifies an extrinsic representation with a particular solution of the scalar logarithmic diffusion equation in one space variable. The result is a single, unified framework to construct an extrinsic representation in R3 of a Ricci flow on a surface of revolution S initialized by a metric g0. Of special interest is the Ricci flow on the torus S1 Ă—S1 embedded in R3. In this case, the extrinsic representation of the Ricci flow on a Riemannian cover of S is eternal. This flow can also be realized as a compact family of nonsmooth, but isometric, embeddings of the torus into R3
A physical application of Kerr-Schild groups
The present work deals with the search of useful physical applications of
some generalized groups of metric transformations. We put forward different
proposals and focus our attention on the implementation of one of them.
Particularly, the results show how one can control very efficiently the kind of
spacetimes related by a Generalized Kerr-Schild (GKS) Ansatz through
Kerr-Schild groups. Finally a preliminar study regarding other generalized
groups of metric transformations is undertaken which is aimed at giving some
hints in new Ans\"atze to finding useful solutions to Einstein's equations.Comment: 18 page
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