Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Black Hole Singularity, Generalized (Holographic) $c$-Theorem and
  Entanglement Negativity   In this paper we revisit the question that in what sense empty $AdS_{5}$
black brane geometry can be thought of as RG-flow. We do this by first
constructing a holographic $c$-function using causal horizon in the black brane
geometry. The UV value of the $c$-function is $a_{UV}$ and then it decreases
monotonically to zero at the curvature singularity. Intuitively, the behavior
of the $c$-function can be understood if we recognize that the dual CFT is in a
thermal state and thermal states are effectively massive with a gap set by the
temperature. In field theory, logarithmic entanglement negativity is an
entanglement measure for mixed states. For example, in two dimensional CFTs on
infinite line at finite temperature, the renormalized entanglement negativity
of an interval has UV (Low- T) value $c_{UV}$ and IR (High-T) value zero. So
this is a potential candidate for our $c$-function. In four dimensions we
expect the same thing to hold on physical grounds. Now since the causal horizon
goes behind the black brane horizon the holographic $c$-function is sensitive
to the physics of the interior. Correspondingly the field theory $c$-function
should also contain information about the interior. So our results suggest that
high temperature (IR) expansion of the negativity (or any candidate
$c$-function) may be a way to probe part of the physics near the singularity.
Negativity at finite temperature depends on the full operator content of the
theory and so perhaps this can be be done in specific cases only.
  The existence of this $c$-function in the bulk is an extreme example of the
paradigm that space-time is built out of entanglement. In particular the fact
that the $c$-function reaches zero at the curvature singularity correlates the
two facts : loss of quantum entanglement in the IR field theory and the end of
geometry in the bulk which in this case is the formation of curvature
singularity.

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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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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: adap-org
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The categories of this paper are: atom-ph
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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: plasm-ph
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The categories of this paper are: econ