Exact solution in the form of a shock wave for the Maxwell and gravitomagnetism equations

Abstract

Over the last halfcentury , much attention in vari� ous fields of mathematical and theoretical physics (1-3) and in applied mathematics (4-7) has been given to approaches providing mathematically rigor� ous results, namely, to the search for exactly solvable models and to rigorous formulations of the original equations of such models as based on fundamental principles. In this work, the method of characteristics is used to construct exact solutions of model problems described by the Maxwell and gravitomagnetism equa� tions for the evolution of the charge or mass density function in spherical or infinite cylindrical domains. The initial charge or mass density distribution in such a domain is radially symmetric, i.e., depends only the radius . In the case of an inhomogeneous initial charge or mass density distribution, we show the existence of a shock wave solution ( Ψ�effect).