Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotics of linear differential systems and application to
  quasi-normal modes of nonrotating black holes   The traditional approach to perturbations of nonrotating black holes in
General Relativity uses the reformulation of the equations of motion into a
radial second-order Schr\"odinger-like equation, whose asymptotic solutions are
elementary. Imposing specific boundary conditions at spatial infinity and near
the horizon defines, in particular, the quasi-normal modes of black holes. For
more complicated equations of motion, as encountered for instance in modified
gravity models with different background solutions and/or additional degrees of
freedom, we present a new approach that analyses directly the first-order
differential system in its original form and extracts the asymptotic behaviour
of perturbations, without resorting to a second-order reformulation. As a
pedagogical illustration, we apply this treatment to the perturbations of
Schwarzschild black holes and then show that the standard quasi-normal modes
can be obtained numerically by solving this first-order system with a spectral
method. This new approach paves the way for a generic treatment of the
asymptotic behaviour of black hole perturbations and the identification of
quasi-normal modes in theories of modified gravity.

4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat