An intrinsic characterization of 2+2 warped spacetimes

We give several equivalent conditions that characterize the 2+2 warped spacetimes: imposing the existence of a Killing-Yano tensor $A$ subject to complementary algebraic restrictions; in terms of the projector $v$ (or of the canonical 2-form $U$) associated with the 2-planes of the warped product. These planes are principal planes of the Weyl and/or Ricci tensors and can be explicitly obtained from them. Therefore, we obtain the necessary and sufficient (local) conditions for a metric tensor to be a 2+2 warped product. These conditions exclusively involve explicit concomitants of the Riemann tensor. We present a similar analysis for the conformally 2+2 product spacetimes and give an invariant classification of them. The warped products correspond to two of these invariant classes. The more degenerate class is the set of product metrics which are also studied from an invariant point of view.Comment: 18 pages; submitted to Class. Quantum Grav

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

Two-dimensional approach to relativistic positioning systems

A relativistic positioning system is a physical realization of a coordinate system consisting in four clocks in arbitrary motion broadcasting their proper times. The basic elements of the relativistic positioning systems are presented in the two-dimensional case. This simplified approach allows to explain and to analyze the properties and interest of these new systems. The positioning system defined by geodesic emitters in flat metric is developed in detail. The information that the data generated by a relativistic positioning system give on the space-time metric interval is analyzed, and the interest of these results in gravimetry is pointed out.Comment: 11 pages, 5 figures. v2: a brief description of the principal bibliography has been adde

Vacuum type I spacetimes and aligned Papapetrou fields: symmetries

We analyze type I vacuum solutions admitting an isometry whose Killing 2--form is aligned with a principal bivector of the Weyl tensor, and we show that these solutions belong to a family of type I metrics which admit a group $G_3$ of isometries. We give a classification of this family and we study the Bianchi type for each class. The classes compatible with an aligned Killing 2--form are also determined. The Szekeres-Brans theorem is extended to non vacuum spacetimes with vanishing Cotton tensor.Comment: 19 pages; a reference adde

On the Weyl transverse frames in type I spacetimes

We apply a covariant and generic procedure to obtain explicit expressions of the transverse frames that a type I spacetime admits in terms of an arbitrary initial frame. We also present a simple and general algorithm to obtain the Weyl scalars $\Psi_2^T$, $\Psi_0^T$ and $\Psi_4^T$ associated with these transverse frames. In both cases it is only necessary to choose a particular root of a cubic expression.Comment: 12 pages, submitted to Gen. Rel. Grav. (6-3-2004

Positioning with stationary emitters in a two-dimensional space-time

The basic elements of the relativistic positioning systems in a two-dimensional space-time have been introduced in a previous work [Phys. Rev. D {\bf 73}, 084017 (2006)] where geodesic positioning systems, constituted by two geodesic emitters, have been considered in a flat space-time. Here, we want to show in what precise senses positioning systems allow to make {\em relativistic gravimetry}. For this purpose, we consider stationary positioning systems, constituted by two uniformly accelerated emitters separated by a constant distance, in two different situations: absence of gravitational field (Minkowski plane) and presence of a gravitational mass (Schwarzschild plane). The physical coordinate system constituted by the electromagnetic signals broadcasting the proper time of the emitters are the so called {\em emission coordinates}, and we show that, in such emission coordinates, the trajectories of the emitters in both situations, absence and presence of a gravitational field, are identical. The interesting point is that, in spite of this fact, particular additional information on the system or on the user allows not only to distinguish both space-times, but also to complete the dynamical description of emitters and user and even to measure the mass of the gravitational field. The precise information under which these dynamical and gravimetric results may be obtained is carefully pointed out.Comment: 14 pages; 5 figure

What can Simbol-X do for gamma-ray binaries?

Gamma-ray binaries have been uncovered as a new class of Galactic objects in the very high energy sky (> 100 GeV). The three systems known today have hard X-ray spectra (photon index ~ 1.5), extended radio emission and a high luminosity in gamma-rays. Recent monitoring campaigns of LSI +61 303 in X-rays have confirmed variability in these systems and revealed a spectral hardening with increasing flux. In a generic one-zone leptonic model, the cooling of relativistic electrons accounts for the main spectral and temporal features observed at high energy. Persistent hard X-ray emission is expected to extend well beyond 10 keV. We explain how Simbol-X will constrain the existing models in connection with Fermi Space Telescope measurements. Because of its unprecedented sensitivity in hard X-rays, Simbol-X will also play a role in the discovery of new gamma-ray binaries, giving new insights into the evolution of compact binaries.Comment: 4 pages, 1 figure, Proceedings of the 2nd International Simbol-X symposium held in Paris, 2-5 December 200

On the invariant symmetries of the D\mathcal{D}-metrics

We analyze the symmetries and other invariant qualities of the $\mathcal{D}$-metrics (type D aligned Einstein Maxwell solutions with cosmological constant whose Debever null principal directions determine shear-free geodesic null congruences). We recover some properties and deduce new ones about their isometry group and about their quadratic first integrals of the geodesic equation, and we analyze when these invariant symmetries characterize the family of metrics. We show that the subfamily of the Kerr-NUT solutions are those admitting a Papapetrou field aligned with the Weyl tensor.Comment: 18 pages; v2: minor change

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