763 research outputs found
Space-time extensions II
The global extendibility of smooth causal geodesically incomplete spacetimes
is investigated. Denote by one of the incomplete non-extendible causal
geodesics of a causal geodesically incomplete spacetime . First, it
is shown that it is always possible to select a synchronised family of causal
geodesics and an open neighbourhood of a final segment
of in such that is comprised by members of ,
and suitable local coordinates can be defined everywhere on
provided that does not terminate either on a tidal force tensor
singularity or on a topological singularity. It is also shown that if, in
addition, the spacetime, , is globally hyperbolic, and the
components of the curvature tensor, and its covariant derivatives up to order
are bounded on , and also the line integrals of the
components of the -order covariant derivatives are finite along the
members of ---where all the components are meant to be registered with
respect to a synchronised frame field on ---then there exists a
extension so that for each , which
is inextendible in , the image, , is
extendible in . Finally, it is also proved that
whenever does terminate on a topological singularity
cannot be generic.Comment: 42 pages, no figures, small changes to match the published versio
Trajectories of the S-matrix poles in Salamon-Vertse potential
The trajectories of S-matrix poles are calculated in the finite-range
phenomenological potential introduced recently by P. Salamon and T. Vertse
(SV). The trajectories of the resonance poles in this SV potential are compared
to the corresponding trajectories in a cut-off Woods-Saxon (WS) potential for
l>0. The dependence on the cut-off radius is demonstrated. The starting points
of the trajectories turn out to be related to the average ranges of the two
terms in the SV potential
Space-Times Admitting Isolated Horizons
We characterize a general solution to the vacuum Einstein equations which
admits isolated horizons. We show it is a non-linear superposition -- in
precise sense -- of the Schwarzschild metric with a certain free data set
propagating tangentially to the horizon. This proves Ashtekar's conjecture
about the structure of spacetime near the isolated horizon. The same
superposition method applied to the Kerr metric gives another class of vacuum
solutions admitting isolated horizons. More generally, a vacuum spacetime
admitting any null, non expanding, shear free surface is characterized. The
results are applied to show that, generically, the non-rotating isolated
horizon does not admit a Killing vector field and a spacetime is not
spherically symmetric near a symmetric horizon.Comment: 11 pages, no figure
Formation of Liesegang patterns: Simulations using a kinetic Ising model
A kinetic Ising model description of Liesegang phenomena is studied using
Monte Carlo simulations. The model takes into account thermal fluctuations,
contains noise in the chemical reactions, and its control parameters are
experimentally accessible. We find that noisy, irregular precipitation takes
place in dimension d=2 while, depending on the values of the control
parameters, either irregular patterns or precipitation bands satisfying the
regular spacing law emerge in d=3.Comment: 7 pages, 8 ps figures, RevTe
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