Static charged spheres with anisotropic pressure in general relativity1J KRISHNA RAO*, M ANNAPURNAf and M M TRIVEDIDepartment of Mathematics, Bhavnagar University, Bhavnagar 364 002, India Abstract We report a generalization of our earlier formalism [Pramana, 54, 663 (1998)] to obtain exact solutions of Einstein-Maxwell's equations for static spheres filled with a charged fluid having anisotropic pressure and of null conductivity. Defining new variables: w = (4p/3) (r+e) r2, u = 4pxr2, vr = 4ppr r2, v^ = 4pp^ r2 [r,x( = -(1/2) F14F14), pr, p^ being respectively the energy densities of matter and electrostatic fields, radial and transverse fluid pressures whereas e denotes the eigenvalue of the conformal Weyl tensor and interpreted as the energy density of the free gravitational field], we have recast Einstein's field equations into a form easy to integrate. Since the system is underdetermined we make the following assumptions to solve the field equations (i) u = vr = (a2/2k)rn+2, v^ = k1vr, w = k2 vr; a2, n( > 0), k1, k2being constants with k = ((k1+2)/3+k2) and (ii) w+u = (b2/2) rn+2, u = vr, v^-vr = k, with b and k as constants. In both cases the field equations are integrated completely. The first solution is regular in the metric as well as physical variables for all values of n > 0. Even though the second solution contains terms like k/r2 since Q(0) = 0 it is argued that the pressure anisotropy, caused by the electric flux near the centre, can be made to vanish reducing it to the generalized Cooperstock-de la Cruz solution given in [14]. The interior solutions are shown to match with the exterior Reissner-Nordstrom solution over a fixed boundary. Keywords Charged static spheres; energy density of the free gravitational field; anisotropic pressure.Pacs No 04.20 Jb |