Hoffmann-Infeld Black Hole Solutions in Lovelock Gravity

Five-dimensional black holes are studied in Lovelock gravity coupled to Hoffmann-Infeld non-linear electrodynamics. It is shown that some of these solutions present a double peak behavior of the temperature as a function of the horizon radius. This feature implies that the evaporation process, though drastic for a period, leads to an eternal black hole remnant. Moreover, the form of the caloric curve corresponds to the existence of a plateau in the evaporation rate, which implies that black holes of intermediate scales turn out to be unstable. The geometrical aspects, such as the absence of conical singularity, the structure of horizons, etc. are also discussed. In particular, solutions that are asymptotically AdS arise for special choices of the parameters, corresponding to charged solutions of five-dimensional Chern-Simons gravity.Comment: 6 pages, 5 figures, Revtex4. References added and comments clarified; version accepted for publicatio

Theoretical confirmation of Feynman's hypothesis on the creation of circular vortices in Bose-Einstein condensates: III

In two preceding papers (Infeld and Senatorski 2003 J. Phys.: Condens. Matter 15 5865, and Senatorski and Infeld 2004 J. Phys.: Condens. Matter 16 6589) the authors confirmed Feynman's hypothesis on how circular vortices can be created from oppositely polarized pairs of linear vortices (first paper), and then gave examples of the creation of several different circular vortices from one linear pair (second paper). Here in part III, we give two classes of examples of how the vortices can interact. The first confirms the intuition that the reconnection processes which join two interacting vortex lines into one, practically do not occur. The second shows that new circular vortices can also be created from pairs of oppositely polarized coaxial circular vortices. This seems to contradict the results for such pairs given in Koplik and Levine 1996 Phys. Rev. Lett. 76 4745.Comment: 10 pages, 7 figure

Nonlinear Electron Oscillations in a Viscous and Resistive Plasma

New non-linear, spatially periodic, long wavelength electrostatic modes of an electron fluid oscillating against a motionless ion fluid (Langmuir waves) are given, with viscous and resistive effects included. The cold plasma approximation is adopted, which requires the wavelength to be sufficiently large. The pertinent requirement valid for large amplitude waves is determined. The general non-linear solution of the continuity and momentum transfer equations for the electron fluid along with Poisson's equation is obtained in simple parametric form. It is shown that in all typical hydrogen plasmas, the influence of plasma resistivity on the modes in question is negligible. Within the limitations of the solution found, the non-linear time evolution of any (periodic) initial electron number density profile n_e(x, t=0) can be determined (examples). For the modes in question, an idealized model of a strictly cold and collisionless plasma is shown to be applicable to any real plasma, provided that the wavelength lambda >> lambda_{min}(n_0,T_e), where n_0 = const and T_e are the equilibrium values of the electron number density and electron temperature. Within this idealized model, the minimum of the initial electron density n_e(x_{min}, t=0) must be larger than half its equilibrium value, n_0/2. Otherwise, the corresponding maximum n_e(x_{max},t=tau_p/2), obtained after half a period of the plasma oscillation blows up. Relaxation of this restriction on n_e(x, t=0) as one decreases lambda, due to the increase of the electron viscosity effects, is examined in detail. Strong plasma viscosity is shown to change considerably the density profile during the time evolution, e.g., by splitting the largest maximum in two.Comment: 16 one column pages, 11 figures, Abstract and Sec. I, extended, Sec. VIII modified, Phys. Rev. E in pres

Shape invariant hypergeometric type operators with application to quantum mechanics

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can be analysed together and the mathematical formalism we use can be extended in order to define other shape invariant operators. All the considered shape invariant operators are directly related to Schrodinger type equations.Comment: More applications available at http://fpcm5.fizica.unibuc.ro/~ncotfa

Einstein-Infeld-Hoffman method and soliton dynamics in a parity noninvariant system

We consider slow motion of a pointlike topological defect (vortex) in the nonlinear Schrodinger equation minimally coupled to Chern-Simons gauge field and subject to external uniform magnetic field. It turns out that a formal expansion of fields in powers of defect velocity yields only the trivial static solution. To obtain a nontrivial solution one has to treat velocities and accelerations as being of the same order. We assume that acceleration is a linear form of velocity. The field equations linearized in velocity uniquely determine the linear relation. It turns out that the only nontrivial solution is the cyclotron motion of the vortex together with the whole condensate. This solution is a perturbative approximation to the center of mass motion known from the theory of magnetic translations.Comment: 6 pages in Latex; shortened version to appear in Phys.Rev.

A Generalization of the Kepler Problem

We construct and analyze a generalization of the Kepler problem. These generalized Kepler problems are parameterized by a triple $(D, \kappa, \mu)$ where the dimension $D\ge 3$ is an integer, the curvature $\kappa$ is a real number, the magnetic charge $\mu$ is a half integer if $D$ is odd and is 0 or 1/2 if $D$ is even. The key to construct these generalized Kepler problems is the observation that the Young powers of the fundamental spinors on a punctured space with cylindrical metric are the right analogues of the Dirac monopoles.Comment: The final version. To appear in J. Yadernaya fizik

Degenerate Four Virtual Soliton Resonance for KP-II

By using disipative version of the second and the third members of AKNS hierarchy, a new method to solve 2+1 dimensional Kadomtsev-Petviashvili (KP-II) equation is proposed. We show that dissipative solitons (dissipatons) of those members give rise to the real solitons of KP-II. From the Hirota bilinear form of the SL(2,R) AKNS flows, we formulate a new bilinear representation for KP-II, by which, one and two soliton solutions are constructed and the resonance character of their mutual interactions is studied. By our bilinear form, we first time created four virtual soliton resonance solution for KP-II and established relations of it with degenerate four-soliton solution in the Hirota-Satsuma bilinear form for KP-II.Comment: 10 pages, 5 figures, Talk on International Conference Nonlinear Physics. Theory and Experiment. III, 24 June-3 July, 2004, Gallipoli(Lecce), Ital

Higher-order-in-spin interaction Hamiltonians for binary black holes from source terms of Kerr geometry in approximate ADM coordinates

The Kerr metric outside the ergosphere is transformed into ADM coordinates up to the orders $1/r^4$ and $a^2$, respectively in radial coordinate $r$ and reduced angular momentum variable $a$, starting from the Kerr solution in quasi-isotropic as well as harmonic coordinates. The distributional source terms for the approximate solution are calculated. To leading order in linear momenta, higher-order-in-spin interaction Hamiltonians for black-hole binaries are derived.Comment: REVTeX4, 20 pages, typos corrected in Eq. (124) and (130

The binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part

Post-Newtonian expansions of the Brill-Lindquist and Misner-Lindquist solutions of the time-symmetric two-black-hole initial value problem are derived. The static Hamiltonians related to the expanded solutions, after identifying the bare masses in both solutions, are found to differ from each other at the third post-Newtonian approximation. By shifting the position variables of the black holes the post-Newtonian expansions of the three metrics can be made to coincide up to the fifth post-Newtonian order resulting in identical static Hamiltonians up the third post-Newtonian approximation. The calculations shed light on previously performed binary point-mass calculations at the third post-Newtonian approximation.Comment: LaTeX, 9 pages, to be submitted to Physical Review

A BPS Interpretation of Shape Invariance

We show that shape invariance appears when a quantum mechanical model is invariant under a centrally extended superalgebra endowed with an additional symmetry generator, which we dub the shift operator. The familiar mathematical and physical results of shape invariance then arise from the BPS structure associated with this shift operator. The shift operator also ensures that there is a one-to-one correspondence between the energy levels of such a model and the energies of the BPS-saturating states. These findings thus provide a more comprehensive algebraic setting for understanding shape invariance.Comment: 15 pages, 2 figures, LaTe