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=(4π/3)(ρ+ε)r2, u=4πξr2, vr=4πprr2, v⊥=4πp⊥r2[ρ, ξ(=−(1/2)F14F14), pr, p⊥ being respectively the energy densities of matter and electrostatic fields, radial and transverse fluid pressures whereas ε 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=(a2/2κ)rn+2, v⊥=k1vr, w=k2vr; a2, n(>0), k1, k2 being constants with κ=((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 . The interior solutions are shown to match with the exterior Reissner-Nordstrom solution over a fixed boundary.
Volume 95, 2021
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