548 research outputs found
On Further Generalization of the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon
A rigidity theorem that applies to smooth electrovac spacetimes which
represent either (A) an asymptotically flat stationary black hole or (B) a
cosmological spacetime with a compact Cauchy horizon ruled by closed null
geodesics was given in a recent work \cite{frw}. Here we enlarge the framework
of the corresponding investigations by allowing the presence of other type of
matter fields. In the first part the matter fields are involved merely
implicitly via the assumption that the dominant energy condition is satisfied.
In the second part Einstein-Klein-Gordon (EKG), Einstein-[non-Abelian] Higgs
(E[nA]H), Einstein-[Maxwell]-Yang-Mills-dilaton (E[M]YMd) and
Einstein-Yang-Mills-Higgs (EYMH) systems are studied. The black hole event
horizon or, respectively, the compact Cauchy horizon of the considered
spacetimes is assumed to be a smooth non-degenerate null hypersurface. It is
proven that there exists a Killing vector field in a one-sided neighborhood of
the horizon in EKG, E[nA]H, E[M]YMd and EYMH spacetimes. This Killing vector
field is normal to the horizon, moreover, the associated matter fields are also
shown to be invariant with respect to it. The presented results provide
generalizations of the rigidity theorems of Hawking (for case A) and of
Moncrief and Isenberg (for case B) and, in turn, they strengthen the validity
of both the black hole rigidity scenario and the strong cosmic censor
conjecture of classical general relativity.Comment: 25 pages, LaTex, a shortened version, including a new proof for lemma
5.1, the additional case of Einstein-Yang-Mills-Higgs systems is also
covered, to appear in Class. Quant. Gra
Front motion in an type reaction-diffusion process: Effects of an electric field
We study the effects of an external electric field on both the motion of the
reaction zone and the spatial distribution of the reaction product, , in an
irreversible reaction-diffusion process. The electrolytes
and are initially separated in space
and the ion-dynamics is described by reaction-diffusion equations obeying local
electroneutrality. Without an electric field, the reaction zone moves
diffusively leaving behind a constant concentration of -s. In the presence
of an electric field which drives the reagents towards the reaction zone, we
find that the reaction zone still moves diffusively but with a diffusion
coefficient which slightly decreases with increasing field. The important
electric field effect is that the concentration of -s is no longer constant
but increases linearly in the direction of the motion of the front. The case of
an electric field of reversed polarity is also discussed and it is found that
the motion of the front has a diffusive, as well as a drift component. The
concentration of -s decreases in the direction of the motion of the front,
up to the complete extinction of the reaction. Possible applications of the
above results to the understanding of the formation of Liesegang patterns in an
electric field is briefly outlined.Comment: 13 pages, 13 figures, submitted to J. Chem. Phy
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
Dynamic Scaling of Width Distribution in Edwards--Wilkinson Type Models of Interface Dynamics
Edwards--Wilkinson type models are studied in 1+1 dimensions and the
time-dependent distribution, P_L(w^2,t), of the square of the width of an
interface, w^2, is calculated for systems of size L. We find that, using a flat
interface as an initial condition, P_L(w^2,t) can be calculated exactly and it
obeys scaling in the form _\infty P_L(w^2,t) = Phi(w^2 / _\infty,
t/L^2) where _\infty is the stationary value of w^2. For more complicated
initial states, scaling is observed only in the large- time limit and the
scaling function depends on the initial amplitude of the longest wavelength
mode. The short-time limit is also interesting since P_L(w^2,t) is found to
closely approximate the log-normal distribution. These results are confirmed by
Monte Carlo simulations on a `roof-top' model of surface evolution.Comment: 5 pages, latex, 3 ps figures in a separate files, submitted to
Phys.Rev.
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
- …