arXiv:gr-qc/9603032v1 21 Mar 1996 PACS 04.20.Jb DROPLETS IN GENERAL RELATIVITY: EXACT SELF-CONSISTENT SOLUTIONS TO THE INTERACTING SCALAR AND ELECTROMAGNETIC FIELD EQUATIONS Yu. P. RYBAKOV and G. N. SHIKIN Department of Theoretical Physics Russian Peoples’ Friendship University 6, Miklukho-Maklay str., 117198 Moscow, Russia e-mail: rybakov@udn.msk.su B. SAHA Laboratory of Theoretical Physics Joint Institute for Nuclear Research, Dubna 141980 Dubna, Moscow region, Russia e-mail: saha@thsun1.jinr.dubna.su It is shown, for the self-consistent system of scalar, electro-magnetic and gravitational fields in general relativity, that the equations of motion admit a special kind of solutions with spherical or cylindrical symmetry. For these solutions, the physical fields vanish and the space-time is flat outside of the critical sphere or cylinder. Therefore, the mass and the electric charge of these configurations are zero. The principal difference between droplet-like solutions with spherical symmetry and those with cylindrical one has been established. In the first case there exists a possibility of continuous transformation of droplet-like configuration into the solitonian one, when for the second case there is no such a possibility.