Universal Maximum Angular Speed for Objects in Flat and Curved Spacetime: Theoretical Upper Bound for Massless and Massive Particles

Abstract We present a rigorous theoretical framework establishing a universal upper bound on angular speed for objects at a given radius, applicable in both flat and curved spacetimes. Starting from the speed- of-light limit in special relativity, we derive the maximum angular speed in flat spacetime as ω-max = c/r. This framework is then generalized to spherically symmetric (Schwarzschild) and axisymmetric spacetimes, including the effects of gravity and frame-dragging. Only massless particles can, in principle, attain this bound under specific conditions such as photon orbits, while massive objects are strictly subluminal. The framework clarifies that ω-max is a theoretical rotational limit and does not imply generic rotation of massless particles. Special cases are analysed, including photon spheres and event horizons, where the maximum angular speed tends to zero due to gravitational infall. Numerical calculations illustrate the bound in flat spacetime, near compact objects, and at the event horizon. This discovery provides a rotational analogue to the linear speed-of-light limit, offering new insight into relativistic kinematics in extreme gravitational environments.