Understanding singularities in Cartan's and NSF geometric structures

In this work we establish a relationship between Cartan's geometric approach to third order ODEs and the 3-dim Null Surface Formulation (NSF). We then generalize both constructions to allow for caustics and singularities that necessarily arise in these formalisms.Comment: 22 pages, 2 figure

Schwarzschild Tests of the Wahlquist-Estabrook-Buchman-Bardeen Tetrad Formulation for Numerical Relativity

A first order symmetric hyperbolic tetrad formulation of the Einstein equations developed by Estabrook and Wahlquist and put into a form suitable for numerical relativity by Buchman and Bardeen (the WEBB formulation) is adapted to explicit spherical symmetry and tested for accuracy and stability in the evolution of spherically symmetric black holes (the Schwarzschild geometry). The lapse and shift which specify the evolution of the coordinates relative to the tetrad congruence are reset at frequent time intervals to keep the constant-time hypersurfaces nearly orthogonal to the tetrad congruence and the spatial coordinate satisfying a kind of minimal rate of strain condition. By arranging through initial conditions that the constant-time hypersurfaces are asymptotically hyperbolic, we simplify the boundary value problem and improve stability of the evolution. Results are obtained for both tetrad gauges (``Nester'' and ``Lorentz'') of the WEBB formalism using finite difference numerical methods. We are able to obtain stable unconstrained evolution with the Nester gauge for certain initial conditions, but not with the Lorentz gauge.Comment: (accepted by Phys. Rev. D) minor changes; typos correcte

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

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.

Symmetric hyperbolic system in the Ashtekar formulation

We present a first-order symmetric hyperbolic system in the Ashtekar formulation of general relativity for vacuum spacetime. We add terms from constraint equations to the evolution equations with appropriate combinations, which is the same technique used by Iriondo, Leguizam\'on and Reula [Phys. Rev. Lett. 79, 4732 (1997)]. However our system is different from theirs in the points that we primarily use Hermiticity of a characteristic matrix of the system to characterize our system "symmetric", discuss the consistency of this system with reality condition, and show the characteristic speeds of the system.Comment: 4 pages, RevTeX, to appear in Phys. Rev. Lett., Comments added, refs update

Structural Evolution of a Composite Middle to Lower Crustal Section: The Sierra de Pie de Palo, Northwest Argentina

The Sierra de Pie de Palo of northwest Argentina preserves middle to lower crustal metamorphic rocks that were penetratively deformed during Ordovician accretion of the Precordillera terrane to the Gondwana margin. New structural, petrologic, and geochronologic data from a 40 km structural transect reveals that the Sierra de Pie de Palo preserves a middle to lower crustal ductile thrust complex consisting of individual structural units and not an intact ophiolite and cover sequence. Top-to-the-west thrusting occurred intermittently on discrete ductile shear zones from ∼515 to ∼417 Ma and generally propagated toward the foreland with progressive deformation. Ordovician crustal shortening and peak metamorphic temperatures in the central portion of the Sierra de Pie de Palo were synchronous with retro-arc shortening and magmatic flare-up within the Famatina arc. Accretion of the Precordillera terrane resulted in the end of arc flare-up and the onset of synconvergent extension by ∼439 Ma. Continued synextensional to postextensional convergence was accommodated along progressively lower grade shear zones following terrane accretion and the establishment of a new plate margin west of the Precordillera terrane. The results support models of Cordilleran orogens that link voluminous arc magmatism to periods of regional shortening. The deformation, metamorphic, and magmatic history within the Sierra de Pie de Palo is consistent with models placing the region adjacent to the Famatina margin in the middle Cambrian and not as basement to the Precordillera terrane