Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A proof of the instability of AdS for the Einstein--null dust system
  with an inner mirror   In 2006, Dafermos and Holzegel formulated the so-called AdS instability
conjecture, stating that there exist arbitrarily small perturbations to AdS
initial data which, under evolution by the Einstein vacuum equations for
$\Lambda<0$ with reflecting boundary conditions on conformal infinity, lead to
the formation of black holes. The numerical study of this conjecture in the
simpler setting of the spherically symmetric Einstein--scalar field system was
initiated by Bizon and Rostworowski, followed by a vast number of numerical and
heuristic works by several authors.
  In this paper, we provide the first rigorous proof of the AdS instability
conjecture in the simplest possible setting, namely for the spherically
symmetric Einstein--massless Vlasov system, in the case when the Vlasov field
is moreover supported only on radial geodesics. This system is equivalent to
the Einstein--null dust system, allowing for both ingoing and outgoing dust. In
order to overcome the break down of this system occuring once the null dust
reaches the centre $r=0$, we place an inner mirror at $r=r_{0}>0$ and study the
evolution of this system on the exterior domain $\{r\ge r_{0}\}$. The structure
of the maximal development and the Cauchy stability properties of general
initial data in this setting are studied in our companion paper.
  The statement of the main theorem is as follows: We construct a family of
mirror radii $r_{0\epsilon}>0$ and initial data $\mathcal{S}_{\epsilon}$,
$\epsilon\in(0,1]$, converging to the AdS initial data in a suitable norm, such
that, for any $\epsilon>0$, the maximal development
$(\mathcal{M}_{\epsilon},g_{\epsilon})$ of $\mathcal{S}_{\epsilon}$ contains a
black hole region. Our proof is based on purely physical space arguments.

24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: eess
7
The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
3
The categories of this paper are: physics