Anisotropic dark matter stars in gravity's rainbow

In this study, we explore the structural and stability properties of anisotropic dark matter stars within the framework of gravity's rainbow. By incorporating energy-dependent rainbow functions into the spacetime metric, we examine quantum gravitational effects on compact stars under extreme conditions. Utilizing a modified Tolman–Oppenheimeer–Volkoff (TOV) formalism, we derive exact analytical solutions and perform numerical simulations to investigate the impact of anisotropy and rainbow parameters on stellar mass, radius, and compactness. Our analysis includes stability criteria such as the static stability condition, adiabatic indices, and sound speed causality, highlighting the dynamic behavior of these stars. The findings reveal that gravity's rainbow allows for more massive and stable compact stars compared to General Relativity, offering insights into quantum gravitational corrections and their astrophysical implications.