The Cavendish Experiment in General Relativity
Solutions of Einstein’s equations are discussed in which the “gravitational force” is balanced by an electrical force, and which can serve as models for the Cavendish experiment.
Equilibrium of charged dust in general relativity
Equilibrium of charged dust is studied in both the classical and relativistic theories. It is already known that the configuration of the dust is arbitrary if the ratio of the charge to mass densities,σ/ρ, is everywhere ± 1 (in relativistic units). I show here that there are equilibrium configurations for certain other valuesσ/ρ, including nonuniform ones. The solutions in these cases are arbitrary up to the choice of a harmonic function and a function of the electrostatic potential. In general they contain singularities.
Stationary gravitational fields of a charged perfect fluid
Einstein’s field equations which include electromagnetism are investigated when the metric admits a timelike Killing motion and the source is a charged perfect fluid under isometric motion. It is shown that the pressure must necessarily be a function of the electrostatic and gravitational potentials. A class of solutions is found under the following simplifying assumptions: (i) The pressure is a constant, (ii) the Lorentz force vanishes, and (iii) the magnetic and twist potentials are functionally related. In this class the ratio of σ/(ρ+3p) is a constant and this resembles an equilibrium condition. Finally a four‐parameter group (maximal) is supplied which can generate new solutions of this class.