Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Growing Hair on the extremal $BTZ$ black hole   We show that the nonlinear $\sigma-$model in an asymptotically $AdS_3$
space-time admits a novel local symmetry. The field action is assumed to be
quartic in the nonlinear $\sigma-$model fields and minimally coupled to
gravity. The local symmetry transformation simultaneously twists the nonlinear
$\sigma-$model fields and changes the space-time metric, and it can be used to
map an extremal $BTZ$ black hole to infinitely many hairy black hole solutions.

8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph