Asymptotically anomalous black hole configurations in gravitating nonlinear electrodynamics

We analyze the class of non-linear electrodynamics minimally coupled to gravitation supporting asymptotically flat \textit{non Schwarzschild-like} elementary solutions. The Lagrangian densities governing the dynamics of these models in flat space are defined and fully characterized as a subclass of the set of functions of the two standard field invariants, restricted by requirements of regularity, parity invariance and positivity of the energy, which are necessary conditions for the theories to be physically admissible. Such requirements allow for a complete characterization and classification of the geometrical structures of the elementary solutions for the corresponding gravity-coupled models. In particular, an immediate consequence of the requirement of positivity of the energy is the asymptotic flatness of gravitating elementary solutions for any admissible model. The present analysis, together with the (already published) one concerning the full class of admissible gravitating non-linear electrodynamics supporting asymptotically flat \textit{Schwarzschild-like} elementary solutions, completes and exhausts the study of the gravitating point-like charge problem for this kind of models.Comment: 12 pages, 6 figures, revtex4, added extra paragraph in conclusions, added some references, added other minor changes, to published in Phys.Rev.

Electrostatic spherically symmetric configurations in gravitating nonlinear electrodynamics

We perform a study of the gravitating electrostatic spherically symmetric (G-ESS) solutions of Einstein field equations minimally coupled to generalized non-linear abelian gauge models in three space dimensions. These models are defined by lagrangian densities which are general functions of the gauge field invariants, restricted by some physical conditions of admissibility. They include the class of non-linear electrodynamics supporting ESS non-topological soliton solutions in absence of gravity. We establish that the qualitative structure of the G-ESS solutions of admissible models is fully characterized by the asymptotic and central-field behaviours of their ESS solutions in flat space (or, equivalently, by the behaviour of the lagrangian densities in vacuum and on the point of the boundary of their domain of definition, where the second gauge invariant vanishes). The structure of these G-ESS configurations for admissible models supporting divergent-energy ESS solutions in flat space is qualitatively the same as in the Reissner-Nordstr\"om case. In contrast, the G-ESS configurations of the models supporting finite-energy ESS solutions in flat space exhibit new qualitative features, which are discussed in terms of the ADM mass, the charge and the soliton energy. Most of the results concerning well known models, such as the electrodynamics of Maxwell, Born-Infeld and the Euler-Heisenberg effective lagrangian of QED, minimally coupled to gravitation, are shown to be corollaries of general statements of this analysis.Comment: 11 pages, revtex4, 4 figures; added references; introduction, conclusions and several sections extended, 2 additional figures included, title change

Work and energy in inertial and non inertial reference frames

It is usual in introductory courses of mechanics to develop the work and energy formalism from Newton's laws. On the other hand, literature analyzes the way in which forces transform under a change of reference frame. Notwithstanding, no analogous study is done for the way in which work and energy transform under those changes of reference frames. We analyze the behavior of energy and work under such transformations and show explicitly the expected invariance of the formalism under Galilean transformations for one particle and a system of particles. The case of non inertial systems is also analyzed and the fictitious works are characterized. In particular, we show that the total fictitious work in the center of mass system vanishes even if the center of mass defines a non inertial frame. Finally, some subtleties that arise from the formalism are illustrated by examples.Comment: 4 pages, 2 figures. LaTeX2e. Part of the approach has been changed but results are unaltered. Version to appear im American Journal of Physic

Screening effects in Relativistic Models of Dense Matter at Finite Temperature

We investigate screening effects of the medium on the potential interaction between two static 'charges' for different models of dense plasmas in the one-boson exchange approximation. The potential can exhibit an oscillatory behavior, which is related to the analytic structure of the corresponding boson propagators in the complex $q$-plane. We have first revisited the one-pion exchange in a nuclear medium. In addition to Friedel oscillations, which are associated to branch cuts in the $q$-plane, there appears another oscillatory component, which arises from a pole on the pion propagator. This pole is located appart from the axes, giving rise to an oscillating Yukawa-like potential. Therefore, we call this phenomenon 'Yukawa oscillations'. This phenomenon does not appear in the Debye component of the QED screened potential, even if the coupling constant is artificially increased. We have also studied a model of QCD quark-gluon plasma. In this case, the one-gluon propagator also shows this kind of poles. At high densities and/or temperatures, where one expects perturbative QCD to be valid, the pole shifts towards large momenta.Comment: Revtex. 9 pages, 9 figure

Electrostatic internal energy using the method of images

For several configurations of charges in the presence of conductors, the method of images permits us to obtain some observables associated with such a configuration by replacing the conductors with some image charges. However, simple inspection shows that the potential energy associated with both systems does not coincide. Nevertheless, it can be shown that for a system of a grounded or neutral conductor and a distribution of charges outside, the external potential energy associated with the real charge distribution embedded in the field generated by the set of image charges is twice the value of the internal potential energy associated with the original system. This assertion is valid for any size and shape of the conductor, and regardless of the configuration of images required. In addition, even in the case in which the conductor is not grounded nor neutral, it is still possible to calculate the internal potential energy of the original configuration through the method of images. These results show that the method of images could also be useful for calculations of the internal potential energy of the original system.Comment: 5 pages, 3 figures. New discussions added. Minor change

Solutions of the dispersion equation in the region of overlapping of zero-sound and particle-hole modes

In this paper the solutions of the zero-sound dispersion equation in the random phase approximation (RPA) are considered. The calculation of the damped zero-sound modes \omega_s(k) (complex frequency of excitation) in the nuclear matter is presented. The method is based on the analytical structure of the polarization operators \Pi(\omega,k). The solutions of two dispersion equations with \Pi(\omega,k) and with Re(\Pi(\omega,k)) are compared. It is shown that in the first case we obtain one-valued smooth solutions without "thumb-like" forms. Considering the giant resonances in the nuclei as zero-sound excitations we compare the experimental energy and escape width of the giant dipole resonance (GDR) in the nucleus A with \omega_s(k) taken at a definite wave vector k=k_A.Comment: 14 pages, 5 figures; revised versio