Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 $M$.

33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
19
The categories of this paper are: eess
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph