Electro-Gravimagnetic Field, Charges and Currents, Inertia Law in Differential Algebra of Biquaternions - Lyudmila Alexeyeva (Fundamental Research and Application of Physical Science Vol. 9, 2023)
One model of electro-gravimagnetic (EGM) field and electro-gravimagnetic charges and currents has been developed based on the biquaternionic generalization of Maxwell and Dirac equations. The connection between them is described by one biquaternionic wave (biwave) equation. Fundamental and regular solutions of this equation are constructed for known charges of currents, as well as in their absence. Using the theory of generalized functions shock EGM waves are considered and the conditions on the fronts of shock waves are obtained. In particular, solutions describing gravitational waves and longitudinal electromagnetic waves are presented. It is shown that the presence of the longitudinal component of EM waves is associated with the density of the EGM field, which is described by the scalar component of the intensity biquaternion. The law of inertia is postulated for free charge-currents in the absence of external EGM fields in the biquaternionic form. The mutual bigradient of such chargescurrents is equal to zero. Its consequence is the well-known laws of conservation of charge and mass. Solutions of this equation are constructed, which describe the objects of dimension N=3,2,1 (particles, body, tissue, fibers). Taken together, these two biwave equations are a closed system for determining the EGM field and the movement of the EGM charges-currents generated by it.