Obtaining the Weyl tensor from the Bel-Robinson tensor

The algebraic study of the Bel-Robinson tensor proposed and initiated in a previous work (Gen. Relativ. Gravit. {\bf 41}, see ref [11]) is achieved. The canonical form of the different algebraic types is obtained in terms of Bel-Robinson eigen-tensors. An algorithmic determination of the Weyl tensor from the Bel-Robinson tensor is presented.Comment: 21 page

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 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

Forward-backward equations for nonlinear propagation in axially-invariant optical systems

We present a novel general framework to deal with forward and backward components of the electromagnetic field in axially-invariant nonlinear optical systems, which include those having any type of linear or nonlinear transverse inhomogeneities. With a minimum amount of approximations, we obtain a system of two first-order equations for forward and backward components explicitly showing the nonlinear couplings among them. The modal approach used allows for an effective reduction of the dimensionality of the original problem from 3+1 (three spatial dimensions plus one time dimension) to 1+1 (one spatial dimension plus one frequency dimension). The new equations can be written in a spinor Dirac-like form, out of which conserved quantities can be calculated in an elegant manner. Finally, these new equations inherently incorporate spatio-temporal couplings, so that they can be easily particularized to deal with purely temporal or purely spatial effects. Nonlinear forward pulse propagation and non-paraxial evolution of spatial structures are analyzed as examples.Comment: 11 page

Heavily obscured AGN with SIMBOL-X

By comparing an optically selected sample of narrow lines AGN with an X-ray selected sample of AGN we have recently derived an estimate of the intrinsic (i.e. before absorption) 2-10 keV luminosity function (XLF) of Compton Thick AGNs. We will use this XLF to derive the number of Compton Thick AGN that will be found in the SIMBOL-X survey(s).Comment: Talk at the Simbol-X symposium held in Paris, 2-5 December, 2008. 6 pages, 1 figure with three panel

Pair-correlation function in 2-dimensional lattice gases

The pair-correlation function in two-dimensional lattice gases is computed by means of three discretized classical equations for the structure of liquids: the hypernetted-chain, the Percus-Yevick, and the crossover integral equations. The equations are numerically solved by an iteration procedure. Two different systems are considered: the Ising-Peierls lattice gas with nearest-neighbor interactions and a model for O adsorbed on the W(110) surface, in which interactions up to the fourth neighbors are taken into account. The values of the pair-correlation function for nearest, next-nearest, and next-next-nearest neighbors are compared with the results of Monte Carlo simulations at four different coverages Θ (Θ=1/8, 1) / 4 ,1/2,3/4) as functions of the lateral coupling. It turns out that the crossover integral equation gives the best agreement with Monte Carlo data in both systems, being accurate especially at low Θ, whereas the Percus-Yevick equation fails in a wide range of parameters

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 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

The emerging population of pulsar wind nebulae in hard X-rays

The hard X-ray synchrotron emission from pulsar wind nebulae (PWNe) probes energetic particles, closely related to the pulsar injection power at the present time. INTEGRAL has disclosed the yet poorly known population of hard X-ray pulsar/PWN systems. We summarize the properties of the class, with emphasys on the first hard X-ray bow-shock (CTB 80 powered by PSR B1951+32), and highlight some prospects for the study of Pulsar Wind Nebulae with the Simbol-X mission.Comment: Proceedings of the 2nd Simbol-X Symposium, AIP Conf. Proc. Series, Eds. P. Ferrando and J. Rodriguez (4 pages, 2 figures