Antonio Bernal

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 whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth global splitting if a spacetime M admits a (continuous) time function t then it admits a smooth (time) function with timelike gradient on all M.

On Smooth Cauchy Hypersurfaces and Geroch’s Splitting Theorem

Given a globally hyperbolic spacetime M, we show the existence of a smooth spacelike Cauchy hypersurface S and, thus, a global diffeomorphism between M and ℝ×S.

Further Results on the Smoothability of Cauchy Hypersurfaces and Cauchy Time Functions

AbstractRecently, folk questions on the smoothability of Cauchy hypersurfaces and time functions of a globally hyperbolic spacetime M, have been solved. Here we give further results, applicable to several problems: (1)Any compact spacelike acausal submanifold H with boundary can be extended to a spacelike Cauchy hypersurface S. If H were only achronal, counterexamples to the smooth extension exist, but a continuous extension (in fact, valid for any compact achronal subset K) is still possible.(2)Given any spacelike Cauchy hypersurface S, a Cauchy temporal function

Leibnizian, Galilean and Newtonian structures of space–time

\mathcal{T}

Dipsogenic potentiation by sodium chloride but not by sucrose or polyethylene glycol in tuberomammillary-mediated polydipsia

(i.e., a smooth function with past-directed timelike gradient everywhere, and Cauchy hypersurfaces as levels) with

On the (non-)uniqueness of the Levi-Civita solution in the Einstein–Hilbert–Palatini formalism

S= \mathcal{T}^{-1}(0)