Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability and instability of the sub-extremal Reissner-Nordstr\"om black
  hole interior for the Einstein-Maxwell-Klein-Gordon equations in spherical
  symmetry   We show non-linear stability and instability results in spherical symmetry
for the interior of a charged black hole -approaching a sub-extremal
Reissner-Nordstr\"om background fast enough at infinity- in presence of a
massive and charged scalar field, motivated by the strong cosmic censorship
conjecture in that setting :
  1. Stability : We prove that spherically symmetric characteristic initial
data to the Einstein-Maxwell- Klein-Gordon equations approaching a
Reissner-Nordstr\"om background with a sufficiently decaying polynomial decay
rate on the event horizon gives rise to a space-time possessing a Cauchy
horizon in a neighbourhood of time-like infinity. Moreover if the decay is even
stronger, we prove that the spacetime metric admits a continuous extension to
the Cauchy horizon. This generalizes the celebrated stability result of
Dafermos for Einstein-Maxwell-real-scalar-field in spherical symmetry.
  2. Instability : We prove that for the class of space-times considered in the
stability part, whose scalar field in addition obeys a polynomial averaged-L^2
(consistent) lower bound on the event horizon, the scalar field obeys an
integrated lower bound transversally to the Cauchy horizon. As a consequence we
prove that the non-degenerate energy is infinite on any null surface crossing
the Cauchy horizon and the curvature of a geodesic vector field blows up at the
Cauchy horizon near time-like infinity. This generalizes an instability result
due to Luk and Oh for Einstein-Maxwell-real-scalar-field in spherical symmetry.
  This instability of the black hole interior can also be viewed as a step
towards the resolution of the C^2 strong cosmic censorship conjecture for
one-ended asymptotically initial data.

26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat