In this paper we consider the generalized uncertainty principle (GUP) in the tunneling formalism via Hamilton-Jacobi method to determine the quantum-corrected Hawking temperature and entropy for noncommutative BTZ black hole. In our results we obtain several types of corrections including the expected logarithmic correction to the area entropy associated with the noncommutative BTZ black holes. We also show that the area entropy product of the noncommutative BTZ black holes is dependent on mass and by analyzing the nature of the specific heat capacity we have observed that the noncommutative BTZ black hole is stable at some range of parameters.

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In this paper we review the AdS/BCFT proposal of T. Takayanagi for holographic description of systems with boundaries, in particular, boundary conformal field theories (BCFTs). Motivated by better understanding of the proposed duality we employ entanglement entropy as a probe of familiar properties of impurities and defects. We discuss configurations, which provide examples of RG flows of the defect entropy as well as RG fixed points. Two interesting observations come out of this analysis of the geometric cartoons of the defect physics. First, entanglement entropy supports the definition of the defect entropy at finite temperature as the Bekenstein-Hawking entropy calculated with respect to a subspace of the horizon. Second, in some examples, geometric data relate entanglement entropy calculations in different dimensions.

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