The role of Finsler-Randers geometry in shaping anisotropic metrics and thermodynamic properties in black holes theory

Abstract

In this research paper, we delve into the study of black hole (BH) structure within the context of Finsler geometry, a novel approach not previously explored by other researchers. We focused on developing the Finsler-Randers metric tensor for black holes, with the aid of the Barthel connection along with the osculating Riemannian method. This newly derived metric demonstrates significant departures from the conventional black hole metrics found in General Relativity (GR) by the presence of Finslerian term $\eta$, thereby shedding new light on the geometry and nature of black holes. To comprehensively understand the characteristics of black holes, we calculated the metric components under both vacuum and non-vacuum conditions. Our findings indicate that the metric structure aligns well with the known Riemannian limits, reinforcing the compatibility of our model with established theories. Moreover, we extended our analysis to include the thermodynamics of black holes in a Finslerian framework in brief. The results from this exploration affirm that the fundamental laws of black hole thermodynamics remain valid, reinforcing the viability and consistency of our Finslerian model. This study not only contributes to our understanding of black hole physics but also opens new avenues for further research in the realm of Finsler geometry and its implications for astrophysics.