Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact Black Hole Solutions with a Conformally Coupled Scalar Field and
  Dynamic Ricci Curvature in $f(R)$ Gravity Theories   We report exact black hole solutions in asymptotically flat or (A)dS
four-dimensional spacetime with a conformally coupled self-interacting scalar
field in $f(R)$ gravity. We first consider the asymptotically flat model $f(R)
= R -2\alpha \sqrt{R}$ and derive an exact black hole solution. Then, we
consider the asymptotically (A)dS model $f(R) =R -2 \Lambda -2 \alpha \sqrt{R-4
\Lambda }$ and derive an exact black hole solution. In both cases the modified
gravity parameter $\alpha$, which has the dimension of the inverse mass, cannot
be set to zero and the self-interacting potential is determined from the
Klein-Gordon equation, preserving the conformal invariance. The thermodynamics
of the solutions is also studied.

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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin