标题： 芬斯勒几何与非交换几何在重力黑洞中的等价性 显示英文标题

标题： The equivalence between Finsler and non-commutative geometries by massive gravity black hole

摘要： 在本工作中，我们想要找到一种可能的方法，以便使非交换几何和芬斯勒几何这两种有用的数学工具之间建立等价关系。基于这一目的，我们致力于通过研究有质量引力黑洞来探索这种可能性。首先介绍了系统的拉格朗日，并通过定义新变量将其重写在非交换的框架下。另一方面，我们关注芬斯勒几何，以期在特定条件下找到一个与上述非交换拉格朗日等价的芬斯勒函数。同时，作为相应条件的一部分，计算了系统的有效势能。 显示英文摘要

摘要： In the present work, we wanted to find the possible way in order to make the equivalence between non-commutative and Finsler geometries as two useful mathematical tools. Based on this purpose, we were concerned to search this possibility by investigating the massive gravity black holes. Firstly the Lagrangian of the system is introduced and then it is rewritten in the non-commutative regime by definition of the new variables. On the other hand, we focus on the Finsler geometry in order to find a Finslerian function which is equivalent to the mentioned non-commutative Lagrangian under special conditions. Also, the effective potential of the system was calculated as a part of the corresponding conditions.