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The extended Einstein-Maxwell-aether-axion model describes internalinteractions inside the system, which contains gravitational, electromagneticfields, the dynamic unit vector field describing the velocity of an aether, andthe pseudoscalar field associated with the axionic dark matter. The specificfeature of this model is that the axion field controls the dynamics of theaether through the guiding functions incorporated into the Jacobson'sconstitutive tensor. Depending on the state of the axion field these guidingfunctions can control and switch on or switch off the influence ofacceleration, shear, vorticity and expansion of the aether flow on the state ofphysical system as a whole. We obtain new exact solutions, which possess thepp-wave symmetry, and indicate them by the term pp-wave aether modes incontrast to the pure pp-waves, which can not propagate in this fieldconglomerate. These exact solutions describe a specific dynamic state of thepseudoscalar field, which corresponds to one of the minima of the axionpotential, and switches off the influence of shear and expansion of the aetherflow; the model does not impose restrictions on the Jacobson's couplingconstants and on the axion mass. Properties of these new exact solutions arediscussed.

The extended Einstein-Maxwell-aether-axion model: Exact solutions for axionically controlled pp-wave aether modes