Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Static spherically symmetric configurations with N non-linear scalar
  fields: global and asymptotic properties   In case of a spherically symmetric non-linear scalar field (SF) in flat
space, besides singularity at the center, spherical singularities can occur for
non-zero values of radial variable $r>0$. We show that in the General
Relativity the gravitational field suppresses the occurrence of the spherical
singularities under some generic conditions. Our consideration deals with
asymptotically flat space-times around static spherically symmetric
configurations in presence of $N$ non-linear SFs, which are minimally coupled
to gravity. Constraints are imposed on the SF potentials, which guarantee a
monotonicity of the fields as functions of radial variable; also the potentials
are assumed to be exponentially bounded. We give direct proof that solutions of
the joint system of Einstein -- SF equations satisfying the conditions of
asymptotic flatness are regular for all values of $r$, except for naked
singularities in the center $r=0$ in the Schwarzschild (curvature) coordinates.
Asymptotic relations for SF and metric near the center are derived, which
appear to be remarkably similar to the case of the Fisher solution for free SF.
These relations determine two main types of the corresponding geodesic
structure when photons can be captured by the singularity or not depending on
the existence of the photon sphere. To illustrate, the case of one SF with
monomial potential is analyzed in detail numerically. We show that the image of
the accretion disk around the singularity, observed from infinity, can take the
form of a bright ring with a dark spot in the center, like the case of an
ordinary black hole.

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The categories of this paper are: math
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys