Electromagnetic mass models in general relativity

The metric coefficients $g_{00}$ and $g_{11}$ of both the Schwarzschild and Reissner-Nordström metrics satisfy the relation $g_{00}{g}_{11}=-1\mathrm{}$. 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-Nordström metric is obtained. This solution represents a charged particle whose mass is entirely of electromagnetic origin.