Static, scalarly charged dust

Abstract

In an earlier work DAS (~) studied the static, coupled, gravitat ional and electrostatic as well as scalar fields due to incoherent dust charged in electric or scalar sense; he found some very general results for such systems. However, in his derivation a funct ional relationship between the metric coefficient goo and the potential 9 is assumed, and an equality of matter and charge densities is imposed, this imposition being justified by Newtonian mechanics. Later DE and RAYCHAUDtIURI (2) found that a funct ional relationship between the three functions go0, r and a/~ (ratio of electric-charge and mass densities) follows directly from the field equations; then the equality of matter and electric-charge densities is found to be the only possible solution in regions free of singularities. Our purpose is to demonstrate tha t goo = exp [J2SI] follows directly from the field equations in the case S is the long-range, repulsive, scalar field produced by a static, scalarly charged dust; and that the equality of densities of matter and scalar charge is also a consequence of the Einstein scalar equations. In the general, static line element