Spacetime Curvature Gradient and the Angular Velocity of Rotation

Author: Zhang Suhang, Luoyang

The spin angular velocity is proportional to the spacetime curvature gradient.

\omega \propto \nabla R

Spacetime curvature determines the spin angular velocity of celestial bodies. The mechanism may be understood as follows: the curvature gradient forms a geometric potential difference, analogous to how an electric potential difference drives electric current or a temperature gradient drives heat flow. The curvature gradient drives rotation. A larger curvature gradient yields a stronger potential difference and a higher spin angular velocity; a smaller curvature gradient yields a weaker potential difference and a lower spin angular velocity. Hence, the spin angular velocity is proportional to the curvature gradient: \omega \propto \nabla R. Further, since angular momentum L = I\omega, we obtain L \propto I\nabla R. This establishes a concrete correspondence between geometric quantities (curvature) and mechanical quantities (angular momentum): the curvature gradient acts as a potential difference; the potential difference drives rotation, and rotation generates angular momentum.