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

TL;DR

This paper explores the potential equivalence between non-commutative and Finsler geometries using massive gravity black holes, by reformulating the Lagrangian and identifying conditions for their correspondence.

Contribution

It introduces a method to establish the equivalence between non-commutative and Finsler geometries through massive gravity black hole models, providing a new mathematical link.

Findings

Derived a non-commutative Lagrangian from massive gravity black holes.

Identified Finslerian functions equivalent to the non-commutative Lagrangian.

Calculated the effective potential under specific conditions.

Abstract

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.