TYPE II CHARGED GENERALISATION OF DURGAPAL’S SOLUTIONS FOR n ≥ 2

Abstract

We investigate the equilibrium configuration of a spherically symmetric charged fluid with a metric of the form ds^2=-e^λ(r) dr^2-r^2 (dθ^2+sin^2⁡θ dϕ^2 )+e^ν(r) dt^2. Using e^ν = A^2 (1 + x)^n where x+Cr^2, the coupled Einstein-Maxwell equations are reformulated in terms of a first-order linear differential equation for Z = e^(-λ). The general solution to this equation is derived, admitting integration constants and coefficients defined through recurrence relations. We explore a specific case with n=2 and an electric filed E^2= (α^2 C_x)/(2(1+x))resulting in explicit expressions for the metric components, matter density ρ and pressure p.