Note on: "Domain wall universe in the Einstein--Born--Infeld theory" Phys. Lett. B 679 (2009) 160

The interaction between bulk and dynamic domain wall in the presence of a linear / non-linear electromagnetism make energy density, tension and pressure on the wall all variables, depending on the wall position. In [1] this fact seems to be ignored.Comment: 4 pages, 1 figur

Ground State H-Atom in Born-Infeld Theory

Within the context of Born-Infeld (BI) nonlinear electrodynamics (NED) we revisit the non-relativistic, spinless H-atom. The pair potential computed from the Born-Infeld equations is approximated by the Morse type potential with remarkable fit over the critical region where the convergence of both the short and long distance expansions slows down dramatically. The Morse potential is employed to determine both the ground state energy of the electron and the BI parameter.Comment: 4 pages, 1 figure, final version to appear in Foundation of Physic

New non-Abelian black hole solutions in Born-Infeld gravity

We introduce new black hole solutions to the Einstein-Yang-Mills-Born-Infeld (EYMBI), Einstein-Yang-Mills-Born-Infeld-Gauss-Bonnet (EYMBIGB) and Einstein-Yang-Mills-Born-Infeld-Gauss-Bonnet-Lovelock (EYMBIGBL) gravities in higher dimensions $N\geq 5$ to investigate the roles of Born-Infeld parameter $\beta$. It is shown that, these solutions in the limits of $\beta \to 0,$ and $\beta \to \infty ,$ represent pure gravity and gravity coupled with Yang-Mills fields, respectively. For $0<\beta <\infty$ it yields a variety of black holes, supporting even regular ones at $r=0$.Comment: 17 pages, 4 figures

Classical and quantum quasi-free position dependent mass; P\"oschl-Teller and ordering-ambiguity

We argue that the classical and quantum mechanical correspondence may play a basic role in the fixation of the ordering-ambiguity parameters. We use quasi-free position-dependent masses in the classical and quantum frameworks. The effective P\"oschl-Teller model is used as a manifested reference potential to elaborate on the reliability of the ordering-ambiguity parameters available in the literature.Comment: 10 page

Dilatonic interpolation between Reissner-Nordstrom and Bertotti-Robinson spacetimes with physical consequences

We give a general class of static, spherically symmetric, non-asymptotically flat and asymptotically non-(anti) de Sitter black hole solutions in Einstein-Maxwell-Dilaton (EMD) theory of gravity in 4-dimensions. In this general study we couple a magnetic Maxwell field with a general dilaton potential, while double Liouville-type potentials are coupled with the gravity. We show that the dilatonic parameters play the key role in switching between the Bertotti-Robinson and Reissner-Nordstr\"om spacetimes. We study the stability of such black holes under a linear radial perturbation, and in this sense we find exceptional cases that the EMD black holes are unstable. In continuation we give a detailed study of the spin-weighted harmonics in dilatonic Hawking radiation spectrum and compare our results with the previously known ones. Finally, we investigate the status of resulting naked singularities of our general solution when probed with quantum test particles.Comment: 27 pages, 4 figures, to appear in CQG

Flatland Position-Dependent-Mass: Polar Coordinates, Separability and Exact Solvability

The kinetic energy operator with position-dependent-mass in plane polar coordinates is obtained. The separability of the corresponding Schr¨odinger equation is discussed. A hypothetical toy model is reported and two exactly solvable examples are studied

Gravitating magnetic monopole in Vaidya geometry

A magnetic-monopole solution of a non-Abelian gauge theory as proposed by 't Hooft and Polyakov is studied in the Vaidya spacetime. We find that the solutions of Einstein equations generates a geometry of the Bonnor-Vaidya corresponding to magnetically charged null fluid with Higgs field contributing a cosmological term. In the absence of the scalar fields the corresponding Wu-Yang solution of the gauge theory still generates the Bonnor-Vaidya geometry, but with no cosmological term.Comment: 5 RevTeX pages, no figures, minor changes, to appear in Physical Review

d-Dimensional generalization of the point canonical transformation for a quantum particle with position-dependent mass

The d-dimensional generalization of the point canonical transformation for a quantum particle endowed with a position-dependent mass in Schrodinger equation is described. Illustrative examples including; the harmonic oscillator, Coulomb, spiked harmonic, Kratzer, Morse oscillator, Poschl-Teller and Hulthen potentials are used as reference potentials to obtain exact energy eigenvalues and eigenfunctions for target potentials at different position-dependent mass settings.Comment: 14 pages, no figures, to appear in J. Phys. A: Math. Ge

Solutions for f(R) gravity coupled with electromagnetic field

In the presence of external, linear / nonlinear electromagnetic fields we integrate f(R) \sim R+2{\alpha}\surd(R+const.) gravity equations. In contrast to their Einsteinian cousins the obtained black holes are non-asymptotically flat with a deficit angle. In proper limits we obtain from our general solution the global monopole solution in f(R) gravity. The scale symmetry breaking term adopted as the nonlinear electromagnetic source adjusts the sign of the mass of the resulting black hole to be physical.Comment: 7 pages no figure, final version for publication in European Physical Journal

Constant curvature f(R) gravity minimally coupled with Yang-Mills field

We consider the particular class of f(R) gravities minimally coupled with Yang - Mills (YM) field in which the Ricci scalar =R_{0}= constant in all dimensions d\geq4. Even in this restricted class the spacetime has unlimited scopes determined by an equation of state of the form P_{eff}={\omega}{\rho}. Depending on the distance from the origin (or horizon of a black hole) the state function {\omega}(r) takes different values. It is observed that {\omega}\rightarrow(1/3) (the ultra relativistic case in 4 - dimensions) and {\omega}\rightarrow-1 (the cosmological constant) are the limiting values of our state function {\omega}(r) in a spacetime centered by a black hole. This suggests that having a constant {\omega} throughout spacetime around a charged black hole in f(R) gravity with constant scalar curvature is a myth.Comment: 12 pages 2 figures, Some references and 2 figures are added with minor changes. Final version for publication in European Physical Journal