Electromagnetic mass models in general relativity

The metric coefficients g₀₀ and g₁₁ of both the Schwarzschild and Reissner-Nordstr\"om metrics satisfy the relation g₀₀g₁₁=-1. A coordinate-independent statement of this relation using the eigenvalues of the Einstein tensor is given. By considering the relation between the metric coefficients to be valid inside a charged perfect-fluid distribution, it is shown that the mass-energy density and the pressure of the distribution are of electromagnetic origin. In the absence of charge, however, there exists no interior solution. A particular solution which confirms the same and matches smoothly with the exterior Reissner-Nordstr\"om metric is obtained. This solution represents a charged particle whose mass is entirely of electromagnetic origin.