Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rotating black holes without $\mathbb{Z}_2$ symmetry and their shadow
  images   The recent detection of gravitational waves from black hole coalescences and
the first image of the black hole shadow enhance the possibilities of testing
gravitational theories in the strong-field regime. In this paper, we study the
physical properties and the shadow image of a class of Kerr-like rotating black
holes, whose $\mathbb{Z}_2$ symmetry is generically broken. Such black hole
solutions could arise in effective low-energy theories of a fundamental quantum
theory of gravity, such as string theory. Within a theory-agnostic framework,
we require that the Kerr-like solutions are asymptotically flat, and assume
that a Carter-like constant is preserved, enabling the geodesic equations to be
fully separable. Subject to these two requirements, we find that the
$\mathbb{Z}_2$ asymmetry of the spacetime is characterized by two arbitrary
functions of polar angle. The shadow image turns out to be $\mathbb{Z}_2$
symmetric on the celestial coordinates. Furthermore, the shadow is completely
blind to one of the arbitrary functions. The other function, although would
affect the apparent size of the shadow, it hardly distorts the shadow contour
and has merely no degeneracy with the spin parameter. Therefore, the parameters
in this function can be constrained with black hole shadows, only when the mass
and the distance of the black hole from the earth are measured with great
precision.

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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con