AN APPLICATION OF RIEMANNIAN GEOMETRY IN THEORETICAL PHYSICS IS CONSIDERED. AS WE WILL SEE BY A SUITABLE GEOMETRIC STRUCTURE ON A ROTATING CHARGED 4-MANIFOLD BY SPACE TIME COORDINATE (T, R, Q, F) CALLED Kerr-NEWMAN GEOMETRY WE WILL DISCUSS AN IMPORTANT TENSOR ON A GIVEN RIEMANNIAN 4-MANIFOLD WHICH IS SO APPLICABLE IN THEORETICAL PHYSICS. WE CONSIDER A ROTATING CHARGED BLACK HOLE AS A SMOOTH RIEMANNIAN 4-MANIFOLD STRUCTURE BY THE SPACE TIME COORDINATE (T, R, Q, F). THEN, BY USING DIFFERENTIAL FORMS AND EXTERIOR DERIVATIVE WE WILL FIND THE CORRESPONDING ELECTROMAGNETIC FIELD TENSOR.