Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geodesic congruences in exact plane wave spacetimes and the memory
  effect   Displacement and velocity memory effects in the exact, vacuum, plane
gravitational wave line element have been studied recently by looking at the
behaviour of pairs of geodesics or via geodesic deviation. Instead, one may
investigate the evolution of geodesic congruences. In our work here, we obtain
the evolution of the kinematic variables which characterise timelike geodesic
congruences, using chosen pulse profiles (square and sech-squared) in the
exact, plane gravitational wave line element. We also analyse the behaviour of
geodesic congruences in possible physical scenarios describable using
derivatives (first, second and third) of one of the chosen pulses. Beginning
with a discussion on the generic behaviour of such congruences and consequences
thereof, we find exact analytical expressions for shear and expansion with the
two chosen pulse profiles. Qualitatively similar numerical results are noted
when various derivatives of the sech-squared pulse are used. We conclude that
for geodesic congruences, a growth (or decay) of shear causes focusing of an
initially parallel congruence, after the departure of the pulse. A correlation
between the `focusing time (or $u$ value, $u$ being the affine parameter)' and
the amplitude of the pulse (or its derivatives) is found. Such features
distinctly suggest a memory effect, named in recent literature as ${\cal B}$
memory.

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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph