411 research outputs found
Geometrical classification of Killing tensors on bidimensional flat manifolds
Valence two Killing tensors in the Euclidean and Minkowski planes are
classified under the action of the group which preserves the type of the
corresponding Killing web. The classification is based on an analysis of the
system of determining partial differential equations for the group invariants
and is entirely algebraic. The approach allows to classify both characteristic
and non characteristic Killing tensors.Comment: 27 pages, 20 figures, pictures format changed to .eps, typos
correcte
Gauss-Bonnet brane gravity with a confining potential
A brane scenario is envisaged in which the -dimensional bulk is endowed
with a Gauss-Bonnet term and localization of matter on the brane is achieved by
means of a confining potential. The resulting Friedmann equations on the brane
are modified by various extra terms that may be interpreted as the X-matter,
providing a possible phenomenological explanation for the accelerated expansion
of the universe. The age of the universe in this scenario is studied and shown
to be consistent with the present observational data.Comment: 14 pages, 4 figures, to appear in PR
On certain classes of solutions of the Weierstrass-Enneper system inducing constant mean curvature surfaces
Analysis of the generalized Weierstrass-Enneper system includes the
estimation of the degree of indeterminancy of the general analytic solution and
the discussion of the boundary value problem. Several different procedures for
constructing certain classes of solutions to this system, including potential,
harmonic and separable types of solutions, are proposed. A technique for
reduction of the Weierstrass-Enneper system to decoupled linear equations, by
subjecting it to certain differential constraints, is presented as well. New
elementary and doubly periodic solutions are found, among them kinks, bumps and
multi-soliton solutions
Distance-redshift from an optical metric that includes absorption
We show that it is possible to equate the intensity reduction of a light wave
caused by weak absorption with a geometrical reduction in intensity caused by a
"transverse" conformal transformation of the spacetime metric in which the wave
travels. We are consequently able to modify Gordon's optical metric to account
for electromagnetic properties of ponderable material whose properties include
both refraction and absorption. Unlike refraction alone however, including
absorption requires a modification of the optical metric that depends on the
eikonal of the wave itself. We derive the distance-redshift relation from the
modified optical metric for Friedman-Lema\^itre-Robertson-Walker spacetimes
whose cosmic fluid has associated refraction and absorption coefficients. We
then fit the current supernovae data and provide an alternate explanation
(other than dark energy) of the apparent acceleration of the universe.Comment: 2 figure
On extra forces from large extra dimensions
The motion of a classical test particle moving on a 4-dimensional brane
embedded in an -dimensional bulk is studied in which the brane is allowed to
fluctuate along the extra dimensions. It is shown that these fluctuations
produce three different forces acting on the particle, all stemming from the
effects of extra dimensions. Interpretations are then offered to describe the
origin of these forces and a relationship between the 4 and -dimensional
mass of the particle is obtained by introducing charges associated with large
extra dimensions.Comment: 9 pages, no figuer
On marginally outer trapped surfaces in stationary and static spacetimes
In this paper we prove that for any spacelike hypersurface containing an
untrapped barrier in a stationary spacetime satisfying the null energy
condition, any marginally outer trapped surface cannot lie in the exterior
region where the stationary Killing vector is timelike. In the static case we
prove that any marginally outer trapped surface cannot penetrate into the
exterior region where the static Killing vector is timelike. In fact, we prove
these result at an initial data level, without even assuming existence of a
spacetime. The proof relies on a powerful theorem by Andersson and Metzger on
existence of an outermost marginally outer trapped surface.Comment: 22 pages, 3 figures; 1 reference added, 1 figure changed, other minor
change
Using 3D Stringy Gravity to Understand the Thurston Conjecture
We present a string inspired 3D Euclidean field theory as the starting point
for a modified Ricci flow analysis of the Thurston conjecture. In addition to
the metric, the theory contains a dilaton, an antisymmetric tensor field and a
Maxwell-Chern Simons field. For constant dilaton, the theory appears to obey a
Birkhoff theorem which allows only nine possible classes of solutions,
depending on the signs of the parameters in the action. Eight of these
correspond to the eight Thurston geometries, while the ninth describes the
metric of a squashed three sphere. It therefore appears that one can construct
modified Ricci flow equations in which the topology of the geometry is encoded
in the parameters of an underlying field theory.Comment: 17 pages, Late
On separable Fokker-Planck equations with a constant diagonal diffusion matrix
We classify (1+3)-dimensional Fokker-Planck equations with a constant
diagonal diffusion matrix that are solvable by the method of separation of
variables. As a result, we get possible forms of the drift coefficients
providing separability of the
corresponding Fokker-Planck equations and carry out variable separation in the
latter. It is established, in particular, that the necessary condition for the
Fokker-Planck equation to be separable is that the drift coefficients must be linear. We also find the necessary condition for
R-separability of the Fokker-Planck equation. Furthermore, exact solutions of
the Fokker-Planck equation with separated variables are constructedComment: 20 pages, LaTe
Asymptotic expansions of the Cotton-York tensor on slices of stationary spacetimes
We discuss expansions for the Cotton-York tensor near infinity for arbitrary
slices of stationary spacetimes. From these expansions it follows directly that
a necessary condition for the existence of conformally flat slices in
stationary solutions is the vanishing of a certain quantity of quadrupolar
nature (obstruction). The obstruction is nonzero for the Kerr solution. Thus,
the Kerr metric admits no conformally flat slices. An analysis of higher orders
in the expansions of the Cotton-York tensor for solutions such that the
obstruction vanishes suggests that the only stationary solution admitting
conformally flat slices are the Schwarzschild family of solutions.Comment: Revised version to appear in Class. Quantum Grav. with 13 pages.
Section 2 regarding multipolar expansions of stationary spacetimes largely
expanded. A Maple script demonstrating the calculations in the axially
symmetric case is available upon request from the autho
Covariant perturbations of domain walls in curved spacetime
A manifestly covariant equation is derived to describe the perturbations in a
domain wall on a given background spacetime. This generalizes recent work on
domain walls in Minkowski space and introduces a framework for examining the
stability of relativistic bubbles in curved spacetimes.Comment: 15 pages,ICN-UNAM-93-0
- âŠ