Einstein's equations in Ashtekar's variables constitute a symmetric hyperbolic system

We show that the 3+1 vacuum Einstein field equations in Ashtekar's variables constitutes a first order symmetric hyperbolic system for arbitrary but fixed lapse and shift fields, by suitable adding to the system terms proportional to the constraint equations.Comment: 4 pages, revte

Long-term solar activity influences on South American rivers

River streamflows are excellent climatic indicators since they integrate precipitation over large areas. Here we follow up on our previous study of the influence of solar activity on the flow of the Parana River, in South America. We find that the unusual minimum of solar activity in recent years have a correlation on very low levels in the Parana's flow, and we report historical evidence of low water levels during the Little Ice Age. We also study data for the streamflow of three other rivers (Colorado, San Juan and Atuel), and snow levels in the Andes. We obtained that, after eliminating the secular trends and smoothing out the solar cycle, there is a strong positive correlation between the residuals of both the Sunspot Number and the streamflows, as we obtained for the Parana. Both results put together imply that higher solar activity corresponds to larger precipitation, both in summer and in wintertime, not only in the large basin of the Parana, but also in the Andean region north of the limit with Patagonia.Comment: Accepted to publication by Journal of Atmospheric and Solar-Terrestrial Physic

Constant Crunch Coordinates for Black Hole Simulations

We reinvestigate the utility of time-independent constant mean curvature foliations for the numerical simulation of a single spherically-symmetric black hole. Each spacelike hypersurface of such a foliation is endowed with the same constant value of the trace of the extrinsic curvature tensor, $K$. Of the three families of $K$-constant surfaces possible (classified according to their asymptotic behaviors), we single out a sub-family of singularity-avoiding surfaces that may be particularly useful, and provide an analytic expression for the closest approach such surfaces make to the singularity. We then utilize a non-zero shift to yield families of $K$-constant surfaces which (1) avoid the black hole singularity, and thus the need to excise the singularity, (2) are asymptotically null, aiding in gravity wave extraction, (3) cover the physically relevant part of the spacetime, (4) are well behaved (regular) across the horizon, and (5) are static under evolution, and therefore have no ``grid stretching/sucking'' pathologies. Preliminary numerical runs demonstrate that we can stably evolve a single spherically-symmetric static black hole using this foliation. We wish to emphasize that this coordinatization produces $K$-constant surfaces for a single black hole spacetime that are regular, static and stable throughout their evolution.Comment: 14 pages, 9 figures. Formatted using Revtex4. To appear Phys. Rev. D 2001, Added numerical results, updated references and revised figure

Exploiting gauge and constraint freedom in hyperbolic formulations of Einstein's equations

We present new many-parameter families of strongly and symmetric hyperbolic formulations of Einstein's equations that include quite general algebraic and live gauge conditions for the lapse. The first system that we present has 30 variables and incorporates an algebraic relationship between the lapse and the determinant of the three metric that generalizes the densitized lapse prescription. The second system has 34 variables and uses a family of live gauges that generalizes the Bona-Masso slicing conditions. These systems have free parameters even after imposing hyperbolicity and are expected to be useful in 3D numerical evolutions. We discuss under what conditions there are no superluminal characteristic speeds

Initial data for gravity coupled to scalar, electromagnetic and Yang-Mills fields

We give ansatze for solving classically the initial value constraints of general relativity minimally coupled to a scalar field, electromagnetism or Yang-Mills theory. The results include both time-symmetric and asymmetric data. The time-asymmetric examples are used to test Penrose's cosmic censorship inequality. We find that the inequality can be violated if only the weak energy condition holds.Comment: 16 pages, RevTeX, references added, presentational changes, version to appear in Phys Rev.

Extending the lifetime of 3D black hole computations with a new hyperbolic system of evolution equations

We present a new many-parameter family of hyperbolic representations of Einstein's equations, which we obtain by a straightforward generalization of previously known systems. We solve the resulting evolution equations numerically for a Schwarzschild black hole in three spatial dimensions, and find that the stability of the simulation is strongly dependent on the form of the equations (i.e. the choice of parameters of the hyperbolic system), independent of the numerics. For an appropriate range of parameters we can evolve a single 3D black hole to $t \simeq 600 M$ -- $1300 M$, and are apparently limited by constraint-violating solutions of the evolution equations. We expect that our method should result in comparable times for evolutions of a binary black hole system.Comment: 11 pages, 2 figures, submitted to PR

Genetic Diversity of Andean Tuber Crop Species in the in situ Microcenter of Huanuco, Peru

peer reviewedAndean tuber crop species oca (Oxalis tuberosa Molina), ulluco (Ullucus tuberosus Caldas), and mashua (Tropaeolum tuberosum Ruiz & Pav.) play major roles in Andean communities. These species show high variability but are threatened with genetic erosion. To study the management of genetic resources of neglected vegetatively propagated crop species, we studied genetic diversity and structure of these species in an in situ diversity microcenter (Huanuco, Peru). A sample of 15 varieties of oca, 15 of ulluco, and 26 of mashua was analyzed with the inter simple sequence repeats (ISSR) molecular markers. Mean genetic distances and global genetic diversities were high for the three species, with higher values for mashua than for oca and ulluco. Assignment technique divided both oca and ulluco samples into two genetic clusters; the mashua sample probably belongs to a single genetic cluster. Inter simple sequence repeats (ISSR) technique showed intravarietal genetic variability for most varieties, suggesting an underestimation of the in situ genetic variability. These results are discussed considering how variation in breeding systems and farmers' practice influenced patterns of genetic diversity. Our findings confirm the hypothesis of a considerable amount of variability found in neglected Andean tubers and are essential to deserve adequate conservation strategies and to maintain genetic resources of neglected Andean tuber crop species under a threat of genetic erosion

Energy Norms and the Stability of the Einstein Evolution Equations

The Einstein evolution equations may be written in a variety of equivalent analytical forms, but numerical solutions of these different formulations display a wide range of growth rates for constraint violations. For symmetric hyperbolic formulations of the equations, an exact expression for the growth rate is derived using an energy norm. This expression agrees with the growth rate determined by numerical solution of the equations. An approximate method for estimating the growth rate is also derived. This estimate can be evaluated algebraically from the initial data, and is shown to exhibit qualitatively the same dependence as the numerically-determined rate on the parameters that specify the formulation of the equations. This simple rate estimate therefore provides a useful tool for finding the most well-behaved forms of the evolution equations.Comment: Corrected typos; to appear in Physical Review

Numerical Relativity: A review

Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of strong field scenarios and been crucial to reveal unexpected phenomena. Considerable efforts are being spent to simulate astrophysically relevant simulations, understand different aspects of the theory and even provide insights in the search for a quantum theory of gravity. In the present article I review the present status of the field of Numerical Relativity, describe the techniques most commonly used and discuss open problems and (some) future prospects.Comment: 2 References added; 1 corrected. 67 pages. To appear in Classical and Quantum Gravity. (uses iopart.cls

The Cauchy Problem for the Einstein Equations

Various aspects of the Cauchy problem for the Einstein equations are surveyed, with the emphasis on local solutions of the evolution equations. Particular attention is payed to giving a clear explanation of conceptual issues which arise in this context. The question of producing reduced systems of equations which are hyperbolic is examined in detail and some new results on that subject are presented. Relevant background from the theory of partial differential equations is also explained at some lengthComment: 98 page