Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The characteristic initial-boundary value problem for the
  Einstein--massless Vlasov system in spherical symmetry   In this paper, we initiate the study of the asymptotically AdS
initial-boundary value problem for the Einstein-massless Vlasov system with
$\Lambda<0$ in spherical symmetry. We will establish the existence and
uniqueness of a maximal future development for the characteristic
initial-boundary value problem in the case when smooth initial data are
prescribed on a future light cone $\mathcal{C}^{+}$ emanating from a point at
$\{r=0\}$ and a reflecting boundary condition is imposed on conformal infinity
$\mathcal{I}$. We will then prove a number of continuation criteria for smooth
solutions of the spherically symmetric Einstein-massless Vlasov system, under
the condition that the ratio $2m/r$ remains small in a neighborhood of
$\{r=0\}$. Finally, we will establish a Cauchy stability statement for Anti-de
Sitter spacetime as a solution of the spherically symmetric Einstein-massless
Vlasov system under initial perturbations which are small only with respect to
a low regularity, scale invariant norm $||\cdot||$. This result will imply, in
particular, a long time of existence statement for $||\cdot||$-small initial
data.
  This paper provides the necessary tools for addressing the AdS instability
conjecture in the setting of the spherically symmetric Einstein--massless
Vlasov system, a task which is carried out in our companion paper. However, the
results of this paper are also of independent interest.

10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
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The categories of this paper are: eess
24
The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg