F. Darabi, K. Atazadeh, A. Rezaei-Aghdam
We obtain general $(2+1)$ dimensional black hole solutions in $f(R)$ theory of gravity by applying the Noether symmetry. Then, we derive generalized anti-de Sitter BTZ type black holes subject to a Noether symmetry. This Noether symmetry is along the vector field $\partial_R$ with a conserved Noether charge associated with the displacement of the cosmological constant. Moreover, we study the thermodynamics of these black holes and show that their entropy can be described by the Cardy-Verlinde formula. This is an evidence for Ads/CFT correspondence in the present $f(R)$ theory of gravity subject to the Noether symmetry.
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http://arxiv.org/abs/1304.2926
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