Stationary Axisymmetric Solutions of the Einstein Equations with Rigidly Rotating Perfect Fluid and Nonlinear Charged Sources

A class of stationary rigidly rotating perfect fluid coupled with nonlinear electromagnetic fields was investigated. An exact solution of the Einstein equations with sources for the Carter B(+) branch was found, for the equation of state 3p + = constant. We use a structural function for the Born-Infeld non-linear electrodynamics which is invariant under duality rotations and a metric possessing a fourparameter group of motions. The solution is of Petrov type D and the eigenvectors of the electromagnetic field are aligned to the DebeverPenrose vectors. PACS: 04.20.Jb; 04.40.+c ∗Supported in part by CONACyT. 1 I. BORN-INFELD NON-LINEAR ELECTRODYNAMICS AND DUALITY ROTATIONS The basic description of the dynamical equations of non-linear electrodynamics within general relativity can be done in terms of the null tetrad formalism according to which the metric is given by g = 2e ⊗ e + 2e ⊗ e, e = e1 (1) where the e ∈ Λ fulfill the Cartan structure equations de = e ∧ Γb = Γbce ∧ e (2) and Γb ∈ Λ satisfy the second structure equations dΓb + Γ a s ∧ Γb = 1 2 R bcde c ∧ e (3) The Riemann curvature components R bcd may be replaced by the Weyl conformal tensor components, which are characterized by five complex curvature coefficients C, and the components of the traceless Ricci tensor Cab = Rab − 1/4gabR where Rab = R abs and R = R a. Non-linear theories of Born Infeld type (B-I) are theories with a hamiltonian function H depending on the invariants of the skew-symmetric tensor Pab, P = 1 4 P Pab Q = 1 4 P̌ Pab P̌ ab = − 2 Pcd where abcd is the Levi-Civita symbol with 1234 = 1.