Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Time Dependent Spacetime in $f(R,T)$ Gravity: Gravitational Collapse   In this note a time dependent spacetime is explored in the background of
$f(R,T)$ gravity via the gravitational collapse of a massive star. The star is
modelled by the Vaidya spacetime which is time dependent in nature. The
coupling of matter with curvature is the key feature of $f(R,T)$ theory and
here we have investigated its effects on a collapsing scenario. Two different
types of models, one involving minimal and the other involving non-minimal
coupling between matter and curvature are considered for our study. Power law
and exponential functionalities are considered as examples to check the outcome
of the gravitational collapse. Our prime objective is to explore the nature of
singularities (black hole or naked singularity) that form as an end state of
the collapse. Existence of outgoing radial null geodesics from the central
singularity was probed and such existence implied the formation of naked
singularities thus defying the cosmic censorship hypothesis. The absence of
such outgoing null geodesics would imply the formation of an event horizon and
the singularity formed becomes a black hole. Conditions under which such
possibilities occur are derived for all the models and sub-models.
Gravitational strength of the singularity is also investigated and the
conditions under which we can get a strong or a weak singularity is derived.
The results obtained are very interesting and may be attributed to the coupling
between curvature and matter. It is seen that for non-minimal coupling there is
a possibility of a globally naked singularity, whereas for a minimal coupling
scenario local nakedness is the only option. It is also found that the
singularity formed can be sufficiently weak in nature, which is cosmologically
desirable.

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The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol