Charge without charge, regular spherically symmetric solutions and the Einstein-Born-Infeld theory

The aim of this paper is to continue the research of JMP 46, 042501 (2005) of regular static spherically symmetric spacetimes in Einstein-Born-Infeld theories from the point of view of the spacetime geometry and the electromagnetic structure. The energy conditions, geodesic completeness and the main features of the horizons of this spacetime are explicitly shown. A new static spherically symmetric dyonic solution in Einstein-Born-Infeld theory with similar good properties as in the regular pure electric and magnetic cases of our previous work, is presented and analyzed. Also, the circumvention of a version of "no go" theorem claiming the non existence of regular electric black holes and other electromagnetic static spherically configurations with regular center is explained by dealing with a more general statement of the problem.Comment: Figures in Int J Theor Phys (Online First

On Vanishing Theorems For Vector Bundle Valued p-Forms And Their Applications

Let $F: [0, \infty) \to [0, \infty)$ be a strictly increasing $C^2$ function with $F(0)=0$. We unify the concepts of $F$-harmonic maps, minimal hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and introduce $F$-Yang-Mills fields, $F$-degree, $F$-lower degree, and generalized Yang-Mills-Born-Infeld fields (with the plus sign or with the minus sign) on manifolds. When $F(t)=t, \frac 1p(2t)^{\frac p2}, \sqrt{1+2t} -1,$ and $1-\sqrt{1-2t},$ the $F$-Yang-Mills field becomes an ordinary Yang-Mills field, $p$-Yang-Mills field, a generalized Yang-Mills-Born-Infeld field with the plus sign, and a generalized Yang-Mills-Born-Infeld field with the minus sign on a manifold respectively. We also introduce the $E_{F,g}-$energy functional (resp. $F$-Yang-Mills functional) and derive the first variational formula of the $E_{F,g}-$energy functional (resp. $F$-Yang-Mills functional) with applications. In a more general frame, we use a unified method to study the stress-energy tensors that arise from calculating the rate of change of various functionals when the metric of the domain or base manifold is changed. These stress-energy tensors, linked to $F$-conservation laws yield monotonicity formulae. A "macroscopic" version of these monotonicity inequalities enables us to derive some Liouville type results and vanishing theorems for $p-$forms with values in vector bundles, and to investigate constant Dirichlet boundary value problems for 1-forms. In particular, we obtain Liouville theorems for $F-$harmonic maps (e.g. $p$-harmonic maps), and $F-$Yang-Mills fields (e.g. generalized Yang-Mills-Born-Infeld fields on manifolds). We also obtain generalized Chern type results for constant mean curvature type equations for $p-$forms on $\Bbb{R}^m$ and on manifolds $M$ with the global doubling property by a different approach. The case $p=0$ and $M=\mathbb{R}^m$ is due to Chern.Comment: 1. This is a revised version with several new sections and an appendix that will appear in Communications in Mathematical Physics. 2. A "microscopic" approach to some of these monotonicity formulae leads to celebrated blow-up techniques and regularity theory in geometric measure theory. 3. Our unique solution of the Dirichlet problems generalizes the work of Karcher and Wood on harmonic map

Rotating Black Branes in the presence of nonlinear electromagnetic field

In this paper, we consider a class of gravity whose action represents itself as a sum of the usual Einstein-Hilbert action with cosmological constant and an $U(1)$ gauge field for which the action is given by a power of the Maxwell invariant. We present a class of the rotating black branes with Ricci flat horizon and show that the presented solutions may be interpreted as black brane solutions with two event horizons, extreme black hole and naked singularity provided the parameters of the solutions are chosen suitably. We investigate the properties of the solutions and find that for the special values of the nonlinear parameter, the solutions are not asymptotically anti-deSitter. At last, we obtain the conserved quantities of the rotating black branes and find that the nonlinear source effects on the electric field, the behavior of spacetime, type of singularity and other quantities.Comment: 7 pages, 5 figures, to appear in EPJ

Theory of Coexistence of Superconductivity and Ferroelectricity : A Dynamical Symmetry Model

We propose and investigate a model for the coexistence of Superconductivity (SC) and Ferroelectricity (FE) based on the dynamical symmetries $su(2)$ for the pseudo-spin SC sector, $h(4)$ for the displaced oscillator FE sector, and $su(2) \otimes h(4)$ for the composite system. We assume a minimal symmetry-allowed coupling, and simplify the hamiltonian using a double mean field approximation (DMFA). A variational coherent state (VCS) trial wave-function is used for the ground state: the energy, and the relevant order parameters for SC and FE are obtained. For positive sign of the SC-FE coupling coefficient, a non-zero value of either order parameter can suppress the other (FE polarization suppresses SC and vice versa). This gives some support to "Matthias' Conjecture" [1964], that SC and FE tend to be mutually exclusive. For such a Ferroelectric Superconductor we predict: a) the SC gap $\Delta$ (and $T_c$) will increase with increasing applied pressure when pressure quenches FE as in many ferroelectrics, and b) the FE polarization will increase with increaesing magnetic field up to $H_c$. The last result is equivalent to the prediction of a new type of Magneto-Electric Effect in a coexistent SC-FE material. Some discussion will be given of the relation of these results to the cuprate superconductors.Comment: 46 page

Elastic and thermodynamic properties of alpha-Bi2O3 at high pressures: Study of mechanical and dynamical stability

[EN] The elastic and thermodynamic properties of the monoclinic polymorph of bismuth oxide (alpha-Bi2O3); aka mineral bismite, have been theoretically investigated both at room pressure and under hydrostatic compression by means of first principles calculations based on density functional theory. In this work, the elastic stiffness coefficients, elastic moduli, Poisson's ratio, B/G ratio, elastic anisotropy indexes (A(B), A(G), A(1), A(2), A(3), Au) and directional dependence of Young modulus and linear compressibility have been obtained. Vickers hardness, and sound wave velocities have been calculated. Our simulations show that bismite has a high elastic anisotropy. alpha-Bi2O3 is a ductile material whose elastic anisotropy increases under compression and presents a stronger ability to resist volume compression than shear deformation at all pressures. Besides, it has a very small minimum thermal conductivity, which is well suited for thermoelectric applications. Finally, the mechanical and dynamical stability of bismite at high pressure has been studied and it has been found that alpha-Bi2O3 becomes mechanically unstable at pressures beyond 19.3 GPa and dynamically unstable above 11.5 GPa. These instabilities could be responsible for the amorphization of bismite observed experimentally between 15 and 20 GPa.This research was supported by the Spanish Ministerio de Economia y Competitividad under Projects MAT2016-75586-C4-2-P/3-P and MAT2015-71070-REDC. P.R.-H. and A.M. acknowledge Red Espanola de SupercomputaciOn (RES) and MALTA-Cluster for the computing time.Gomis, O.; Manjón, F.; Rodríguez-Hernández, P.; Muñoz, A. (2019). Elastic and thermodynamic properties of alpha-Bi2O3 at high pressures: Study of mechanical and dynamical stability. Journal of Physics and Chemistry of Solids. 124:111-120. https://doi.org/10.1016/j.jpcs.2018.09.002S11112012

InBO3 and ScBO3 at high pressures: an ab initio study of elastic and thermodynamic properties

We have theoretically investigated the elastic properties of calcite-type orthoborates ABO(3) (A= Sc and In) at high pressure by means of ab initio total-energy calculations. From the elastic stiffness coefficients, we have obtained the elastic moduli (B, G and E), Poisson's ratio (nu), B/G ratio, universal elastic anisotropy index (A(U)), Vickers hardness, and sound wave velocities for both orthoborates. Our simulations show that both borates are more resistive to volume compression than to shear deformation (B > G). Both compounds are ductile and become more ductile, with an increasing elastic anisotropy, as pressure increases. We have also calculated some thermodynamic properties, like Debye temperature and minimum thermal conductivity. Finally, we have evaluated the theoretical mechanical stability of both borates at high hydrostatic pressures. It has been found that the calcite-type structure of InBO3 and ScBO3 becomes mechanically unstable at pressures beyond 56.2 and 57.7 GPa, respectively. (C) 2016 Elsevier Ltd. All rights reserved.This study is supported by the Spanish MICINN projects MAT2013-46649-C4-2-P/3-P and MAT2015-71070-REDC. H.M.O., A.M., and P.R-H. acknowledge computing time provided by Red Espanola de Supercomputacion (RES) and MALTA-Cluster. J.A.S. acknowledges Juan de la Cierva fellowship program for financial support.Gomis, O.; Ortiz, HM.; Sans Tresserras, JÁ.; Manjón Herrera, FJ.; Santamaría-Pérez, D.; Rodríguez-Hernández, P.; Muñoz, A. (2016). InBO3 and ScBO3 at high pressures: an ab initio study of elastic and thermodynamic properties. Journal of Physics and Chemistry of Solids. 98:198-208. https://doi.org/10.1016/j.jpcs.2016.07.002S1982089

Curved momentum spaces from quantum groups with cosmological constant

We bring the concept that quantum symmetries describe theories with nontrivial momentum space properties one step further, looking at quantum symmetries of spacetime in presence of a nonvanish-ing cosmological constant . In particular, the momentum space associated to the κ-deformation of the de Sitter algebra in (1 +1)and (2 +1)dimensions is explicitly constructed as a dual Poisson–Lie group manifold parametrized by . Such momentum space includes both the momenta associated to spacetime translations and the ‘hyperbolic’ momenta associated to boost transformations, and has the geometry of (half of) a de Sitter manifold. Known results for the momentum space of the κ-Poincaré algebra are smoothly recovered in the limit →0, where hyperbolic momenta decouple from translational mo-menta. The approach here presented is general and can be applied to other quantum deformations of kinematical symmetries, including (3 +1)-dimensional ones.A.B., I.G-S and F.J.H. have been partially supported by Ministerio de Economía y Competitividad (MINECO, Spain) under grants MTM2013-43820-P and MTM2016-79639-P (AEI/FEDER, UE), by Junta de Castilla y León (Spain) under grants BU278U14 and VA057U16 and by the Action MP1405 QSPACE from the European Cooperation in Science and Technology (COST). G.G. acknowledges support from the John Templeton Foundation through grant Nr. 4763