Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the splitting problem for Lorentzian manifolds with an
  $\mathbb{R}$-action with causal orbits   We study the interplay between the global causal and geometric structures of
a spacetime $(M,g)$ and the features of a given smooth $\mathbb{R}$-action
$\rho$ on $M$ whose orbits are all causal curves, building on classic results
about Lie group actions on manifolds described by Palais. In the first part of
this paper, we prove that $\rho$ is free and proper (so that $M$ splits
topologically) provided that $(M,g)$ is strongly causal and $\rho$ does not
have what we call weakly ancestral pairs, a notion which admits a natural
interpretation in terms of "cosmic censorship". Accordingly, such condition
holds automatically if $(M,g)$ is globally hyperbolic. We also prove that $M$
splits topologically if $(M,g)$ is strongly causal and $\rho$ is the flow of a
complete conformal Killing causal vector field. In the second part, we
investigate the class of Brinkmann spacetimes, which can be regarded as null
analogues of stationary spacetimes in which $\rho$ is the flow of a complete
parallel null vector field. Inspired by the geometric characterization of
stationary spacetimes in terms of standard stationary ones [24], we obtain an
analogous geometric characterization of when a Brinkmann spacetime is isometric
to a standard Brinkmann spacetime. This result naturally leads us to discuss a
conjectural null analogue for Ricci-flat $4$-dimensional Brinkmann spacetimes
of a celebrated rigidity theorem by Anderson [1], and highlight its relation
with a long-standing 1962 conjecture by Ehlers and Kundt [13]. If true, our
conjecture provides strong mathematical support to the idea that gravitational
plane waves are the most natural "boundary conditions" at infinity for vacuum
solutions of the Einstein equation modeling regions outside gravitationally
radiating sources.

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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph