Charged Weyssenhoff fluid spheres in Einstein–Cartan–Maxwell theory: a general algorithm

Abstract We construct exact static, spherically symmetric charged fluid solutions within the framework of Einstein–Cartan–Maxwell (ECM) theory, in which intrinsic spin and spacetime torsion are incorporated through the Weyssenhoff spin fluid. Starting from the general ECM field equations, a single master differential equation for the gravitational potential $$Z=e^{\nu /2}$$ Z = e ν / 2 is derived. This equation forms the basis of a simple and systematic algorithm for generating charged extensions of known uncharged perfect-fluid solutions. By introducing a deformation of the temporal metric potential, two distinct classes of charged configurations are obtained, depending on whether the deformation parameters $$\alpha $$ α or $$\beta $$ β vanish. The algorithm is applied explicitly to Adler’s interior solution, yielding closed-form expressions for the electric field, charge density, and matter variables, including explicit spin–torsion contributions. Matching the resulting charged Einstein–Cartan (EC) interior solutions to the exterior Reissner–Nordström spacetime fixes all integration constants uniquely in terms of the mass–radius ratio $$\epsilon =m/a$$ ϵ = m / a and the dimensionless charge parameter $$n^{2}=q^{2}/a^{2}$$ n 2 = q 2 / a 2 . In the limit $$n^{2}\rightarrow 0$$ n 2 → 0 , the charged EC configurations reduce smoothly to Adler’s original uncharged interior solution, ensuring the internal consistency of the construction.