Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A proof of Price's Law on Schwarzschild black hole manifolds for all
  angular momenta   Price's Law states that linear perturbations of a Schwarzschild black hole
fall off as $t^{-2\ell-3}$ for $t \to \infty$ provided the initial data decay
sufficiently fast at spatial infinity. Moreover, if the perturbations are
initially static (i.e., their time derivative is zero), then the decay is
predicted to be $t^{-2\ell-4}$. We give a proof of $t^{-2\ell-2}$ decay for
general data in the form of weighted $L^1$ to $L^\infty$ bounds for solutions
of the Regge--Wheeler equation. For initially static perturbations we obtain
$t^{-2\ell-3}$. The proof is based on an integral representation of the
solution which follows from self--adjoint spectral theory. We apply two
different perturbative arguments in order to construct the corresponding
spectral measure and the decay bounds are obtained by appropriate oscillatory
integral estimates.

9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th