Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of Schwarzschild-AdS for the spherically symmetric
  Einstein-Klein-Gordon system   In this paper, we study the global behavior of solutions to the spherically
symmetric coupled Einstein-Klein-Gordon (EKG) system in the presence of a
negative cosmological constant. We prove that the Schwarzschild-AdS spacetimes
(the trivial black hole solutions of the EKG system for which $\phi=0$
identically) are asymptotically stable: Small perturbations of
Schwarzschild-AdS initial data again lead to regular black holes, with the
metric on the black hole exterior approaching a Schwarzschild-AdS spacetime.
The main difficulties in the proof arise from the lack of monotonicity for the
Hawking mass and the asymptotically AdS boundary conditions, which render even
(part of) the orbital stability intricate. These issues are resolved in a
bootstrap argument on the black hole exterior, with the redshift effect and
weighted Hardy inequalities playing the fundamental role in the analysis. Both
integrated decay and pointwise decay estimates are obtained.

15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci