Geodesics of Finsler Hayward black hole surrounded by quintessence

This research paper delves into examining the Hayward black hole structure surrounded by quintessence within the framework of Finsler geometry. Our focus centers on the Finsler metric tensor development for black holes. This newly derived metric introduces significant deviations from regular black hole metrics found in general relativity due to the Finslerian term γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document} presence, thus shedding fresh insights into the geometry and nature of black holes. Our findings reveal that the metric structure aligns closely with known Riemannian limits, affirming the congeniality of our model with existing theories. Furthermore, we extended our analysis to derive critical mass values and determine the normalization factor for the Hayward black hole within the Finlserian framework. The study encompasses a detailed description of the horizons and extremal conditions of the Hayward black hole surrounded by quintessence and the impact of the Finsler parameter γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document} on them. Specifically, we explore the case where the quintessence state parameter is set to ω=-2/3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega = -2/3$$\end{document}. Our analysis delves into the effective potential, providing insights into null geodesics for various energy levels and examining the behavior of horizons by utilizing the definition of the effective potential. We also discuss the impact of γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document} for the same. We compute and analyze the radius of circular orbits, the period, the instability characteristics of circular orbits, and the force acting on photons with the newly introduced parameter γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document} within the quintessence field. We have thoroughly looked over the obtained results and discussed them. Additionally, we explore the shadow of the black hole in this context. Thereby, the validity and consistency of our Finslerian model are strengthened. In addition to increasing our understanding of black hole physics, this study paves the way for further research in the Finsler geometry domain and its applications in astrophysics.