403 research outputs found
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
where the dimension is an integer, the curvature is a real
number, the magnetic charge is a half integer if is odd and is 0 or
1/2 if 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
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
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 and , respectively in radial coordinate and
reduced angular momentum variable , 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
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
- …