Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Black Holes in Higher Dimensional Gravity Theory with Quadratic in
  Curvature Corrections   Static spherically symmetric black holes are discussed in the framework of
higher dimensional gravity with quadratic in curvature terms. Such terms
naturally arise as a result of quantum corrections induced by quantum fields
propagating in the gravitational background. We focus our attention on the
correction of the form ${\cal C}^2=C_{\alpha\beta\gamma\delta}
C^{\alpha\beta\gamma\delta}$. The Gauss-Bonnet equation in four-dimensional
(4D) spacetime enables one to reduce this term in the action to the terms
quadratic in the Ricci tensor and scalar curvature. As a result the
Schwarzschild solution which is Ricci flat will be also a solution of the
theory with the Weyl scalar ${\cal C}^2$ correction. An important new feature
of the spaces with dimension $D > 4$ is that in the presence of the Weyl
curvature-squared term a solution necessary differs from the corresponding
`classical' vacuum Tangherlini metric. This difference is related to the
presence of {\em secondary} or {\em induced} hair. We explore how the
Tangherlini solution is modified by `quantum corrections', assuming that the
gravitational radius $r_0$ is much larger than the scale of the quantum
corrections. We also demonstrated that finding a general solution beyond the
perturbation method can be reduced to solving a single third order ODE (master
equation).

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The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs