We investigate the effect of noncommutativity and quantum corrections to the temperature and entropy of a BTZ black hole based on a Lorentzian distribution with the generalized uncertainty principle (GUP). To determine the Hawking radiation in the tunneling formalism, we apply the Hamilton-Jacobi method by using the Wentzel-Kramers-Brillouin (WKB) approach. In the present study, we have obtained logarithmic corrections to entropy due to the effect of noncommutativity and GUP. We also address the issue concerning stability of the noncommutative BTZ black hole by investigating its modified specific heat capacity.

中文翻译：

---

GUP对BTZ黑洞熵的非交换校正。

我们基于广义不确定性原理（GUP），基于洛伦兹分布，研究了非交换性和量子校正对BTZ黑洞的温度和熵的影响。为了确定隧道形式主义中的霍金辐射，我们通过使用Wentzel-Kramers-Brillouin（WKB）方法应用Hamilton-Jacobi方法。在本研究中，由于非可交换性和GUP的影响，我们获得了熵的对数校正。我们还通过研究非交换BTZ黑洞的比热容来解决其稳定性问题。