[en] A detailed study is presented of the counterrotating model (CRM) for generic finite static axially symmetric thin disks with nonzero radial pressure. A general constraint over the counterrotating tangential velocities, needed to cast the surface energy-momentum tensor of the disk as the superposition of two counterrotating perfect fluids, and expressions for the energy density and pressure of the counterrotating fluids are obtained. We show that, in general, it is not possible to take the two counterrotating fluids as circulating along geodesics nor take the two counterrotating tangential velocities as equal and opposite. A simple family of disks is studied that admits some CRMs with well defined counterrotating tangential velocities and stable against radial perturbations

[en] A detailed study is presented of the counterrotating model (CRM) for generic electrovacuum static axially symmetric relativistic thin disks without radial pressure. We find a general constraint over the counterrotating tangential velocities needed to cast the surface energy-momentum tensor of the disk as the superposition of two counterrotating charged dust fluids. We also find explicit expressions for the energy densities, charge densities and velocities of the counterrotating fluids. We then show that this constraint can be satisfied if we take the two counterrotating streams as circulating along electrogeodesics. However, we show that, in general, it is not possible to take the two counterrotating fluids as circulating along electrogeodesics nor take the two counterrotating tangential velocities as equal and opposite. Four simple families of models of counterrotating charged disks based on Chazy-Curzon-type, Zipoy-Voorhees-type, Bonnor-Sackfield-type, and Kerr-type electrovacuum solutions are considered where we obtain some disks with a CRM well behaved. The models are constructed using the well-known 'displace, cut and reflect' method extended to solutions of vacuum Einstein-Maxwell equations

[en] The interpretation of a family of electrovacuum stationary Taub-NUT-type fields in terms of finite charged perfect fluid disks is presented. The interpretation is made by means of an 'inverse problem' approach used to obtain disk sources of known solutions of the Einstein or Einstein-Maxwell equations. The diagonalization of the energy-momentum tensor of the disks is facilitated in this case by the fact that it can be written as an upper right triangular matrix. We find that the inclusion of electromagnetic fields changes significantly the different material properties of the disks and so we can obtain, for some values of the parameters, finite charged perfect fluid disks that are in agreement with all the energy conditions

[en] The interpretation of some electrovacuum spacetimes in terms of counterrotating perfect fluid discs is presented. The interpretation is made by means of an 'inverse problem' approach used to obtain disc sources of known static solutions of the Einstein-Maxwell equations. In order to do such an interpretation, a detailed study is presented of the counterrotating model (CRM) for generic electrovacuum static axially symmetric relativistic thin discs with nonzero radial pressure. Four simple families of models of counterrotating charged discs based on Chazy-Curzon-type, Zipoy-Voorhees-type, Bonnor-Sackfield-type and charged and magnetized Darmois electrovacuum metrics are considered, where we obtain some discs with a well-behaved CRM

[en] We present two formulations of Fokker-Planck-Rosenbluth-type (FPR) equations for many-particle self-gravitating systems, with first-order relativistic corrections in the post-Newtonian approach (1PN). The first starts from a covariant Fokker-Planck equation for a simple gas, introduced recently by Chacon-Acosta and Kremer (2007 Phys. Rev. E 76 021201). The second derivation is based on the establishment of an 1PN-BBGKY hierarchy, developed systematically from the 1PN microscopic law of force and using the Klimontovich-Dupree (KD) method. We close the hierarchy by the introduction of a two-point correlation function that describes adequately the relaxation process. This picture reveals an aspect that is not considered in the first formulation: the contribution of ternary correlation patterns to the diffusion coefficients, as a consequence of the nature of 1PN interaction. Both formulations can be considered as a generalization of the equation derived by Rezania and Sobouti (2000 Astron. Astrophys. 354 1110), to stellar systems where the relativistic effects of gravitation play a significant role

[en] A method to construct exact general relativistic thick disks that is a simple generalization of the 'displace, cut, and reflect' method commonly used in Newtonian, as well as, in Einstein theory of gravitation is presented. This generalization consists in the addition of a new step in the above mentioned method. The new method can be pictured as a 'displace, cut, fill, and reflect' method. In the Newtonian case, the method is illustrated in some detail with the Kuzmin-Toomre disk. We obtain a thick disk with acceptable physical properties. In the relativistic case two solutions of the Weyl equations, the Weyl gamma metric (also known as the Zipoy-Voorhees metric) and the Chazy-Curzon metric, are used to construct thick disks. Also, the Schwarzschild metric in isotropic coordinates is employed to construct another family of thick disks. In all the considered cases we have nontrivial ranges of the involved parameter that yield thick disks in which all the energy conditions are satisfied

[en] An infinite family of relativistic finite thin disk model with magnetic field is presented. The model is obtained for solving the Einstein-Maxwell equations for static spacetimes by means of the Horsky-Mitskievitch generating conjecture. The vacuum limit of these obtained solutions is the well known Morgan and Morgan solution. The obtained expressions are simply written in terms of oblate spheroidal coordinates. The mass of the disks are finite and the energy-momentum tensor agrees with all the energy conditions. The magnetic field and the circular velocity are evaluated explicitly. All the physical quantities obtained shown an acceptable behavior

[en] We obtain a purely local characterization that singles out the Majumdar-Papapetrou class, the near-horizon Bertotti-Robinson geometry and the Reissner-Nordstroem exterior solution, together with its plane and hyperbolic counterparts, among the static electrovacuum spacetimes. These five classes are found to form the whole set of static Einstein-Maxwell fields without sources and conformally flat space of orbits, that is, the conformastat electrovacuum spacetimes. The main part of the proof consists in showing that a functional relationship between the gravitational and electromagnetic potentials must always exist. The classification procedure also provides an improved characterization of Majumdar-Papapetrou, by only requiring a conformally flat space of orbits with a vanishing Ricci scalar of the usual conveniently rescaled 3-metric. A simple global consideration allows us to state that the asymptotically flat subset of the Majumdar-Papapetrou class and the Reissner-Nordstroem exterior solution are the only asymptotically flat conformastat electrovacuum spacetimes.

[en] We present the first step towards the complete solution of the Einstein-Maxwell equations outside the sources of static spacetimes in which the space of orbits is conformally flat. Under the assumption of functional dependence between the two potentials that define the geometry and the electromagnetic field, the solution consists only of the well known class which depends on a function satisfying the Laplace equation in flat 3-space plus four explicit bi-parametric families of line-elements.

[en] We find the complete solution of the Einstein-Maxwell field equations without sources for static spacetimes in which the space of Killing trajectories is conformally flat. The result is used to present an improved local characterisation of the Majumdar-Papapetrou class of solutions.