5,016 research outputs found
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 admits a smooth
time function whose levels are spacelike Cauchy hyperfurfaces and, thus,
also a smooth global splitting , , (b) if a spacetime admits a (continuous) time
function (i.e., it is stably causal) then it admits a smooth (time)
function with timelike gradient on all .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 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 (gauge field) which parallelizes and \h. Fixed
any vector field of observers Z (), an explicit Koszul--type
formula which reconstruct bijectively all the possible 's from the
gravitational and vorticity 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 ). 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
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