Development of general functional form of the gravitational potential: Addressing the Flatness Problem in Galactic Rotation Curves

This letter presents a mathematical model that may help address the long-standing problem of galaxy rotation curves. The strategy involves exploring the variation of circular velocity `v' with respect to radial distance `r' as a result of which a Bessel differential equation is developed, yielding a general functional form of the potential as a Bessel function. Employing this potential in the case of galaxies, we find the velocity profile in terms of Bessel functions. This approach establishes Bessel functions as a powerful choice for investigating galactic rotation and deepening our understanding of the universe.