Maximum Angular Speed in Flat and Curved Space-Time: A Radius-Dependent Relativistic Framework

<p><strong>Abstract</strong></p> <p>In classical and relativistic mechanics, the speed of light c is regarded as the fundamental upper bound on linear speed for any massive or massless particle. However, the question of whether there exists a corresponding universal bound on angular speed ω has received comparatively little attention. In this work, we propose and analyse a theoretical framework for a Maximum Angular Speed Theory applicable to both flat (Minkowskian) and curved (general relativistic) spacetimes. We begin by establishing the kinematical constraints on rotational motion in special relativity, demonstrating that the requirement</p> <p>v = rω < c</p> <p>imposes a radius-dependent maximum angular speed</p> <p>ω(max) = c / r</p> <p>for any physical orbit. Extending this reasoning to general relativity, we examine the Schwarzschild and Kerr geometries, showing how the curvature of spacetime modifies the effective angular speed limits for test particles and photons near strong gravitational fields. In particular, we show that near the event horizon, the notion of an attainable angular speed for timelike observers vanishes, whereas null trajectories remain governed by horizon-specific geometric conditions. The theory presented herein unifies flat and curved spacetime rotational dynamics under a single principle, and provides new insights into the relationship between angular motion, causality, and relativistic horizons. Potential applications are discussed in astrophysical contexts such as accretion disks, black hole stability, and frame-dragging phenomena. Our analysis suggests that the existence of a maximum angular speed constitutes a fundamental relativistic constraint, complementing the well-established bound on linear speed.</p> <p><strong> </strong></p>