Exploring compact stellar structures in Finsler–Randers geometry with the Barthel connection

Abstract This study introduces a pioneering approach to analyzing compact stars through Finslerian geometry, which has not been previously explored in this context. By employing the Barthel connection within Finsler–Randers spaces, the research derives a novel metric for compact stars, utilizing the unique geometric nature of spacetime inherent in Finslerian geometry. This offers a fresh perspective on understanding the structure of these stars, departing from the traditional Riemannian geometry commonly used in astrophysics. Specifically, the investigation delves into the Randers metric within Finslerian geometry to investigate the dynamics of these celestial bodies. It defines a component of Randers space, denoted as (r) =a+br^2R^{2} η (r) = a + b r 2 R 2, where a and b are constants, r represents radial distance, and R signifies the observed radius of the star. The research focuses on developing metric potentials within the Finslerian framework, enabling a comprehensive comparative analysis of their regularity. By leveraging the unique physical properties of compact stars, the study determines the values of constants “a” and “b, ” as well as those associated with metric potentials. Through an analysis of four distinct compact stars, the research provides valuable insights into various physical attributes based on estimated data. Furthermore, the investigation explores thermodynamic quantities derived within the Finslerian framework, contributing to the characterization of these compact stars. The study emphasizes the stability inherent in the configuration of compact stars under Finsler space geometry, indicating the potential applicability of Finsler geometry in understanding and characterizing celestial bodies in astrophysics.