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 A+B→CA+B\to C 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, $C$, in an irreversible $A^- +B^+ \to C$ reaction-diffusion process. The electrolytes $A\equiv (A^+,A^-)$ and $B\equiv (B^+,B^-)$ 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 $C$-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 $C$-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 $C$-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