Gravity of magnetic stresses and energy

In the framework of designing laboratory tests of relativistic gravity, we investigate the gravitational field produced by the magnetic field of a solenoid. Observing this field might provide a means of testing whether stresses gravitate as predicted by Einstein’s theory. A previous study of this problem by Braginsky, Caves, and Thorne predicted that the contribution to the gravitational field resulting from the stresses of the magnetic field and of the solenoid walls would cancel the gravitational field produced by the mass-energy of the magnetic field, resulting in a null magnetically generated gravitational force outside the solenoid. They claim that this null result, once proved experimentally, would demonstrate the stress contribution to gravity. We show that this result is incorrect, as it arises from an incomplete analysis of the stresses, which neglects the axial stresses in the walls. Once the stresses are properly evaluated, we find that the gravitational field outside a long solenoid is in fact independent of Maxwell and material stresses, and it coincides with the Newtonian field produced by the linear mass distribution equivalent to the density of magnetic energy stored in a unit length of the solenoid. We argue that the gravity of Maxwell stress can be directly measured in the vacuum region inside the solenoid, where the Newtonian noise is absent in principle, and the gravity generated by Maxwell stresses is not screened by the negative gravity of magnetic-induced stresses in the solenoid walls.