Fast and Slow solutions in General Relativity: The Initialization Procedure

We apply recent results in the theory of PDE, specifically in problems with two different time scales, on Einstein's equations near their Newtonian limit. The results imply a justification to Postnewtonian approximations when initialization procedures to different orders are made on the initial data. We determine up to what order initialization is needed in order to detect the contribution to the quadrupole moment due to the slow motion of a massive body as distinct from initial data contributions to fast solutions and prove that such initialization is compatible with the constraint equations. Using the results mentioned the first Postnewtonian equations and their solutions in terms of Green functions are presented in order to indicate how to proceed in calculations with this approach.Comment: 14 pages, Late

Asymptotically constrained and real-valued system based on Ashtekar's variables

We present a set of dynamical equations based on Ashtekar's extension of the Einstein equation. The system forces the space-time to evolve to the manifold that satisfies the constraint equations or the reality conditions or both as the attractor against perturbative errors. This is an application of the idea by Brodbeck, Frittelli, Huebner and Reula who constructed an asymptotically stable (i.e., constrained) system for the Einstein equation, adding dissipative forces in the extended space. The obtained systems may be useful for future numerical studies using Ashtekar's variables.Comment: added comments, 6 pages, RevTeX, to appear in PRD Rapid Com

Integrating Singular Functions on the Sphere

We obtain rigorous results concerning the evaluation of integrals on the two sphere using complex methods. It is shown that for regular as well as singular functions which admit poles, the integral can be reduced to the calculation of residues through a limiting procedure.Comment: 15 pages, revte

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

Assessment of healthy and harmful Maillard reaction products in a novel coffee cascara beverage: Melanoidins and acrylamide

Our research aimed to evaluate the formation of Maillard reaction products in sun-dried coffee cascara and their impact on the safety and health promoting properties of a novel beverage called “Instant Cascara” (IC) derived from this coffee by-product. Maillard reaction products in sun-dried coffee cascara have never been reported. “Instant Cascara” (IC) extract was obtained by aqueous extraction and freeze-drying. Proteins, amino acids, lipids, fatty acid profile, sugars, fiber, minerals, and vitamins were analyzed for its nutritional characterization. Acrylamide and caffeine were used as chemical indicators of safety. Colored compounds, also called melanoidins, their stability under 40 °C and in light, and their in vitro antioxidant capacity were also studied. A safe instant beverage with antioxidant properties was obtained to which the following nutritional claims can be assigned: “low fat”, “low sugar” “high fiber” and “source of potassium, magnesium and vitamin C”. For the first time, cascara beverage color was attributed to the presence of antioxidant melanoidins (>10 kDa). IC is a potential sustainable alternative for instant coffee, with low caffeine and acrylamide levels and a healthy composition of nutrients and antioxidants.Fil: Iriondo DeHond, Amaia. Consejo Superior de Investigaciones Científicas. Instituto de Investigación en Ciencias de la Alimentación; EspañaFil: Elizondo, Ana Sofía. Consejo Superior de Investigaciones Científicas. Instituto de Investigación en Ciencias de la Alimentación; EspañaFil: Iriondo DeHond, Maite. Instituto Madrileño de Investigación y Desarrollo Rural; EspañaFil: Ríos, Maria Belén. Consejo Superior de Investigaciones Científicas. Instituto de Investigación en Ciencias de la Alimentación; EspañaFil: Mufari, Jesica Romina. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto de Ciencias y Tecnología de los Alimentos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones Biológicas y Tecnológicas. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Instituto de Investigaciones Biológicas y Tecnológicas; Argentina. Consejo Superior de Investigaciones Científicas. Instituto de Investigación en Ciencias de la Alimentación; EspañaFil: Mendiola, Jose A.. Consejo Superior de Investigaciones Científicas. Instituto de Investigación en Ciencias de la Alimentación; EspañaFil: Ibañez, Elena. Consejo Superior de Investigaciones Científicas. Instituto de Investigación en Ciencias de la Alimentación; EspañaFil: del Castillo, Maria Dolores. Consejo Superior de Investigaciones Científicas. Instituto de Investigación en Ciencias de la Alimentación; Españ