Abstract: As the 'relativistic lever paradox' is a characteristic topic in the theory of relativity application to rotation processes, a covariant four-tensor equation is developed to describe the relativistic rigid-rotation of an extended body subjected to external torques, and its Lorentz transformation between frames S and S¯ in the standard configuration is analysed, to discuss this paradox. From the four-tensor rotation equation applied to an L-shaped body submitted to several torques it is concluded that although the system does not vary its angular momentum in frame S - in which simultaneously applied forces resultant torque is zero -, in frame S¯, it does vary its angular momentum and exerted torque on it is non-zero. From this formalism (asynchronous formulation of relativity), in frame S¯, angular momentum variation is related to Einstein's inertia of energy principle, and the non-zero torque is a consequence of the relativity of simultaneity, showing that this description is coherent and that there is no paradox.
