523 research outputs found
Gravitational Effects on Domain Walls with Curvature Correction
We derive the effective action for a domain wall with small thickness in
curved spacetime and show that, apart from the Nambu term, it includes a
contribution proportional to the induced curvature. We then use this action to
study the dynamics of a spherical thick bubble of false vacuum (de Sitter)
surrounded by an infinite region of true vacuum (Schwarzschild)
An analytical approximation scheme to two point boundary value problems of ordinary differential equations
A new (algebraic) approximation scheme to find {\sl global} solutions of two
point boundary value problems of ordinary differential equations (ODE's) is
presented. The method is applicable for both linear and nonlinear (coupled)
ODE's whose solutions are analytic near one of the boundary points. It is based
on replacing the original ODE's by a sequence of auxiliary first order
polynomial ODE's with constant coefficients. The coefficients in the auxiliary
ODE's are uniquely determined from the local behaviour of the solution in the
neighbourhood of one of the boundary points. To obtain the parameters of the
global (connecting) solutions analytic at one of the boundary points, reduces
to find the appropriate zeros of algebraic equations. The power of the method
is illustrated by computing the approximate values of the ``connecting
parameters'' for a number of nonlinear ODE's arising in various problems in
field theory. We treat in particular the static and rotationally symmetric
global vortex, the skyrmion, the Nielsen-Olesen vortex, as well as the 't
Hooft-Polyakov magnetic monopole. The total energy of the skyrmion and of the
monopole is also computed by the new method. We also consider some ODE's coming
from the exact renormalization group. The ground state energy level of the
anharmonic oscillator is also computed for arbitrary coupling strengths with
good precision.Comment: 5 pages, 3 tables, Late
Some results on homoclinic and heteroclinic connections in planar systems
Consider a family of planar systems depending on two parameters and
having at most one limit cycle. Assume that the limit cycle disappears at some
homoclinic (or heteroclinic) connection when We present a method
that allows to obtain a sequence of explicit algebraic lower and upper bounds
for the bifurcation set The method is applied to two quadratic
families, one of them is the well-known Bogdanov-Takens system. One of the
results that we obtain for this system is the bifurcation curve for small
values of , given by . We obtain
the new three terms from purely algebraic calculations, without evaluating
Melnikov functions
Cosmic strings in axionic-dilatonic gravity
We first consider local cosmic strings in dilaton-axion gravity and show that
they are singular solutions. Then we take a supermassive Higgs limit and
present expressions for the fields at far distances from the core by applying a
Pecci-Quinn and a duality transformation to the dilatonic Melvin's magnetic
universe.Comment: Latex file. 16 page
Macrodimers: ultralong range Rydberg molecules
We study long range interactions between two Rydberg atoms and predict the
existence of ultralong range Rydberg dimers with equilibrium distances of many
thousand Bohr radii. We calculate the dispersion coefficients ,
and for two rubidium atoms in the same excited level , and find
that they scale like , and , respectively. We show that
for certain molecular symmetries, these coefficients lead to long range
potential wells that can support molecular bound levels. Such macrodimers would
be very sensitive to their environment, and could probe weak interactions. We
suggest experiments to detect these macrodimers.Comment: 4 pages, submitted to PR
Electrostatics in a simple wormhole revisited
The electrostatic potential generated by a point charge at rest in a simple
static, spherically symmetric wormhole is given in the form of series of
multipoles and in closed form. The general potential which is physically
acceptable depends on a parameter due to the fact that the monopole solution is
arbitrary. When the wormhole has Z2-symmetry, the potential is completely
determined. The calculation of the electrostatic self-energy and of the
self-force is performed in all cases considered.Comment: 16 pages, no figure
Light Rays at Optical Black Holes in Moving Media
Light experiences a non-uniformly moving medium as an effective gravitational
field, endowed with an effective metric tensor , being the refractive index and the
four-velocity of the medium. Leonhardt and Piwnicki [Phys. Rev. A {\bf 60},
4301 (1999)] argued that a flowing dielectric fluid of this kind can be used to
generate an 'optical black hole'. In the Leonhardt-Piwnicki model, only a
vortex flow was considered. It was later pointed out by Visser [Phys. Rev.
Lett. {\bf 85}, 5252 (2000)] that in order to form a proper optical black hole
containing an event horizon, it becomes necessary to add an inward radial
velocity component to the vortex flow. In the present paper we undertake this
task: we consider a full spiral flow, consisting of a vortex component plus a
radially infalling component. Light propagates in such a dielectric medium in a
way similar to that occurring around a rotating black hole. We calculate, and
show graphically, the effective potential versus the radial distance from the
vortex singularity, and show that the spiral flow can always capture light in
both a positive, and a negative, inverse impact parameter interval. The
existence of a genuine event horizon is found to depend on the strength of the
radial flow, relative to the strength of the azimuthal flow. A limitation of
our fluid model is that it is nondispersive.Comment: 30 pages, LaTeX, 4 ps figures. Expanded discussion especially in
section 6; 5 new references. Version to appear in Phys. Rev.
Potential--density pairs for spherical galaxies and bulges: the influence of scalar fields
A family of potential--density pairs has been found for spherical halos and
bulges of galaxies in the Newtonian limit of scalar--tensor theories of
gravity. The scalar field is described by a Klein--Gordon equation with a
source that is coupled to the standard Poisson equation of Newtonian gravity.
The net gravitational force is given by two contributions: the standard
Newtonian potential plus a term stemming from massive scalar fields. General
solutions have been found for spherical systems. In particular, we compute
potential--density pairs of spherical galactic systems, and some other
astrophysical quantities that are relevant to generating initial conditions for
spherical galaxy simulations.Comment: Paper accepted for publication in MNRAS, with four figure
Large Scale Cosmic Microwave Background Anisotropies and Dark Energy
In this note we investigate the effects of perturbations in a dark energy
component with a constant equation of state on large scale cosmic microwave
background anisotropies. The inclusion of perturbations increases the large
scale power. We investigate more speculative dark energy models with w<-1 and
find the opposite behaviour. Overall the inclusion of perturbations in the dark
energy component increases the degeneracies. We generalise the parameterization
of the dark energy fluctuations to allow for an arbitrary const ant sound
speeds and show how constraints from cosmic microwave background experiments
change if this is included. Combining cosmic microwave background with large
scale structure, Hubble parameter and Supernovae observations we obtain
w=-1.02+-0.16 (1 sigma) as a constraint on the equation of state, which is
almost independent of the sound speed chosen. With the presented analysis we
find no significant constraint on the constant speed of sound of the dark
energy component.Comment: 7 pages, 8 figures, minor changes to match version accepted for
publication in MNRA
D-Dimensional Radiative Plasma: A Kinetic Approach
The covariant kinetic approach for the radiative plasma, a mixture of a
relativistic moving gas plus radiation quanta (photons, neutrinos, or
gravitons) is generalized to D spatial dimensions. The operational and physical
meaning of Eckart's temperature is reexamined and the D-dimensional expressions
for the transport coefficients (heat conduction, bulk and shear viscosity) are
explicitly evaluated to first order in the mean free time of the radiation
quanta. Weinberg's conclusion that the mixture behaves like a relativistic
imperfect simple fluid (in Eckart's formulation) depends neither on the number
of spatial dimensions nor on the details of the collisional term. The case of
Thomson scaterring is studied in detail, and some consequences for higher
dimensional cosmologies are also discussed.Comment: 28 pages, 1 figure, uses REVTE
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