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

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

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

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

Conformal proper times according to the Woodhouse causal axiomatics of relativistic spacetimes

On the basis of the Woodhouse causal axiomatics, we show that conformal proper times and an extra variable in addition to those of space and time, precisely and physically identified from experimental examples, together give a physical justification for the `chronometric hypothesis' of general relativity. Indeed, we show that, with a lack of these latter two ingredients, no clock paradox solution exists in which the clock and message functions are solely at the origin of the asymmetry. These proper times originate from a given conformal structure of the spacetime when ascribing different compatible projective structures to each Woodhouse particle, and then, each defines a specific Weylian sheaf structure. In addition, the proper time parameterizations, as two point functions, cannot be defined irrespective of the processes in the relative changes of physical characteristics. These processes are included via path-dependent conformal scale factors, which act like sockets for any kind of physical interaction and also represent the values of the variable associated with the extra dimension. As such, the differential aging differs far beyond the first and second clock effects in Weyl geometries, with the latter finally appearing to not be suitable.Comment: 25 pages, 2 figure

Kerr-Schild Symmetries

We study continuous groups of generalized Kerr-Schild transformations and the vector fields that generate them in any n-dimensional manifold with a Lorentzian metric. We prove that all these vector fields can be intrinsically characterized and that they constitute a Lie algebra if the null deformation direction is fixed. The properties of these Lie algebras are briefly analyzed and we show that they are generically finite-dimensional but that they may have infinite dimension in some relevant situations. The most general vector fields of the above type are explicitly constructed for the following cases: any two-dimensional metric, the general spherically symmetric metric and deformation direction, and the flat metric with parallel or cylindrical deformation directions.Comment: 15 pages, no figures, LaTe

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

Large Angle Hadron Correlations from Medium-Induced Gluon Radiation

Final state medium-induced gluon radiation in ultradense nuclear matter is examined and shown to favor large angle emission when compared to vacuum bremsstrahlung due to the suppression of collinear gluons. Perturbative expression for the contribution of its hadronic fragments to the back-to-back particle correlations is derived. It is found that in the limit of large jet energy loss gluon radiation determines the yield and angular distribution of | Delta phi | > Pi/2 di-hadrons to transverse momenta pT2 of the associated particles. Clear transition from enhancement to suppression of the away-side hadron correlations is established at moderate pT2 and its experimentally accessible features are predicted versus the trigger particle momentum pT1.Comment: 5 pages, 3 figures. Figures 1 and 2 and some of the text revised. Footnote added. As published in Phys. Lett.