Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes

The folk questions in Lorentzian Geometry, which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spacetime $(M,g)$ admits a smooth time function $\tau$ whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth global splitting $M= \R \times {\cal S}$, $g= - \beta(\tau,x) d\tau^2 + \bar g_\tau$, (b) if a spacetime $M$ admits a (continuous) time function $t$ (i.e., it is stably causal) then it admits a smooth (time) function $\tau$ with timelike gradient $\nabla \tau$ on all $M$.Comment: 9 pages, Latex, to appear in Commun. Math. Phys. Some comments on time functions and stably causal spacetimes are incorporated, and referred to gr-qc/0411143 for further detail

Leibnizian, Galilean and Newtonian structures of spacetime

The following three geometrical structures on a manifold are studied in detail: (1) Leibnizian: a non-vanishing 1-form $\Omega$ plus a Riemannian metric \h on its annhilator vector bundle. In particular, the possible dimensions of the automorphism group of a Leibnizian G-structure are characterized. (2) Galilean: Leibnizian structure endowed with an affine connection $\nabla$ (gauge field) which parallelizes $\Omega$ and \h. Fixed any vector field of observers Z ($\Omega (Z) = 1$), an explicit Koszul--type formula which reconstruct bijectively all the possible $\nabla$'s from the gravitational ${\cal G} = \nabla_Z Z$ and vorticity $\omega = rot Z/2$ fields (plus eventually the torsion) is provided. (3) Newtonian: Galilean structure with \h flat and a field of observers Z which is inertial (its flow preserves the Leibnizian structure and $\omega = 0$). Classical concepts in Newtonian theory are revisited and discussed.Comment: Minor errata corrected, to appear in J. Math. Phys.; 22 pages including a table, Late

Structural evolution of an alkali sulfate activated slag cement

In this study, the effect of sodium sulfate content and curing duration (from fresh paste up to 18 months) on the binder structure of sodium sulfate activated slag cements was evaluated. Isothermal calorimetry results showed an induction period spanning the first three days after mixing, followed by an acceleration-deceleration peak corresponding to the formation of bulk reaction products. Ettringite, a calcium aluminium silicate hydrate (C-A-S-H) phase, and a hydrotalcite-like Mg-Al layered double hydroxide have been identified as the main reaction products, independent of the Na2SO4 dose. No changes in the phase assemblage were detected in the samples with curing from 1 month up to 18 months, indicating a stable binder structure. The most significant changes upon curing at advanced ages observed were growth of the AFt phase and an increase in silicate chain length in the C-A-S-H, resulting in higher strength