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The Maxwell-Proca electrodynamics corresponding to a finite photon mass causes a substantial change of the Maxwell stress tensor and, under certain circumstances, may cause the electromagnetic stresses to act effectively as "negative pressure." The paper describes a model where this negative pressure imitates gravitational pull and may produce forces comparable to gravity and even become dominant. The effect is associated with the random magnetic fields in the galactic disk with a scale exceeding the photon Compton wavelength. The presence of a weaker regular field does not affect the forces under consideration. The stresses act predominantly on the interstellar gas and cause an additional force pulling the gas towards the center and towards the galactic plane. The stars do not experience any significant direct force but get involved in this process via a "recycling loop" where rapidly evolving massive stars are formed from the gas undergoing galactic rotation and then lose their masses back to the gas within a time shorter than roughly 1/6 of the rotation period. This makes their dynamics inseparable from that of the rotating gas. The lighter, slowly evolving stars, as soon as they are formed, lose connection to the gas and are confined within the galaxy only gravitationally. Numerical examples based on the parameters of our galaxy reveal both opportunities and challenges of this model and motivate further analysis. The critical issue is the plausibility of formation of the irregular magnetic field that would be force free. Another challenge is developing a predictive model of the evolution of the gaseous and stellar population of the galaxy under the aforementioned scenario. It may be interesting to also explore possible broader cosmological implications of the negative-pressure model.

A Hypothetical Effect of the Maxwell–Proca Electromagnetic Stresses on Galaxy Rotation Curves