A hollow rotor shaft for a rotor of an electrical machine may include a cylinder barrel closed off by face flanges on both sides. The cylinder barrel may enclose a shaft cavity. A shaft journal may be configured on each face flanges. An inlet may be disposed in one of the shaft journals by way of which a cooling fluid may pass into the shaft cavity and onto an inner surface of the cylinder barrel. A distribution element may be disposed in the shaft cavity. The distribution element may receive the cooling fluid that enters through the inlet, conduct the cooling fluid in a direction of the inner surface of the cylinder barrel by way of a rotation-symmetrical drainage surface, and give off the cooling fluid to the inner surface by way of a mouth region.