Spherically symmetric static solutions of the Einstein-Maxwell equations

We report a new formalism to obtain solutions of Einstein-Maxwell's equatio ns for static spheres assuming the matter content to be a charged perfect f luid of null-conductivity. Defining three new variables u = 4 pi epsilon r( 2), v = 4 pi pr(2) and w = (4 pi/3)(rho + epsilon)r(2) where epsilon, rho a nd epsilon denote respectively energy densities of the electric, matter and free gravitational fields whereas p is the fluid pressure, Einstein's fiel d equations are rewritten in an elegant form. The solutions given by Bonnor [1], Nduka [2], Cooperstock and De la Cruz [3], Mehra [4], Tikekar [5, 6], Xingxiang [7], Patino and Page [8] are all shown to possess simple relatio ns between u, v, and w whereas Pant and Sah's [9] solution for which all th e three functions, u, v, and w are constants is a trivial case of the prese nt formalism, We have presented six new solutions with epsilon = 2 rho. For the first three solutions w and u are constants with v as a variable where as the remaining three solutions satisfy the equation of state for isotherm al gas; v = kw = -ku where (i) k is an arbitrary constant but not equal to 1 or 1/3 (ii) k = 1 and (iii) k = 1/3. We also obtained a generalization of Cooperstock and De la Cruz's [3] solution which is regular for 2 rho > eps ilon but singular for 2 rho less than or equal to epsilon.