Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gauge invariant perturbations of self-similar Lema\^itre-Tolman-Bondi
  spacetime: even parity modes with $l\geq 2$   In this paper we consider gauge invariant linear perturbations of the metric
and matter tensors describing the self-similar Lema\^itre-Tolman-Bondi
(timelike dust) spacetime containing a naked singularity. We decompose the
angular part of the perturbation in terms of spherical harmonics and perform a
Mellin transform to reduce the perturbation equations to a set of ordinary
differential equations with singular points. We fix initial data so the
perturbation is finite on the axis and the past null cone of the singularity,
and follow the perturbation modes up to the Cauchy horizon. There we argue that
certain scalars formed from the modes of the perturbation remain finite,
indicating linear stability of the Cauchy horizon.

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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: math
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int