Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Casimir effect in the curved background and the black hole in three
  dimensions   We consider the quantum correction to the Lagrangean by the massless free
boson in the curved background in three dimensions where one of the coordinates
is periodic. The correction term is given by an expansion of the metric with
respect to the derivative and the first term expresses to the usual Casimir
energy. As an application, we investigate the change of the geometry in three
dimensional black hole due to the quantum effect and we show that the geometry
becomes like that of the Reissner-Nordstr\o m solution.

3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph