Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hidden symmetry of the static response of black holes: Applications to
  Love numbers   We show that any static linear perturbations around a spherically symmetric
black hole enjoys a set of conserved charges which forms a centrally extended
Schr\"{o}dinger algebra sh(1)=sl$(2,\mathbb{R})\ltimes \mathcal{H}$. The
central charge is given by the black hole mass, echoing results on black hole
entropy from near-horizon diffeomorphism symmetry. The finite symmetry
transformations generated by these conserved charges correspond to Galilean and
conformal transformations of the static field and of the coordinates. This new
structure allows one to discuss the static response of a Schwarzschild black
hole in the test field approximation from a \textit{ symmetry-based approach}.
First we show that the (horizontal) symmetry protecting the vanishing of the
Love numbers recently exhibited by Hui et al coincides with one of the
sl($2,\mathbb{R}$) generators of the Schr\"{o}dinger group. Then, it is
demonstrated that the HJPSS symmetry is selected thanks to the spontaneous
breaking of the full Schr\"{o}dinger symmetry at the horizon down to a simple
abelian sub-group. The latter can be understood as the symmetry protecting the
regularity of the test field at the horizon. In the 4-dimensional case, this
provides a symmetry protection for the vanishing of the Schwarzschild Love
numbers.

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The categories of this paper are: comp-gas
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
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The categories of this paper are: eess
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs