Equilibrium condition for two charged bodies in gravitation theory

The steady-state gravitational field created by combining two spherically symmetric solutions to the equations of an arbitrary scalar-tensor theory of gravity is investigated. The superposition of the fields of two sources located at the origin is examined for combinations involving class 1 and class 2 fields as well as class 2 and class 3 fields; it is found that the resulting field is not spherically symmetric in both cases. The class 2 field of two bodies situated on the z-axis is considered, and a condition is determined under which two charged sources will be in equilibrium. The motion of a charged test particle in the spherically symmetric field of a charged source is analyzed, effects of a scalar field are studied, and a condition is obtained under which the test particle will be at rest relative to the central body.