Abstrae. The covariant Weyl (spin s = 1/2) and Maxwell (s = 1) equations in certain local charts (U, 9 ) of a space-time ( M , g ) are considered. It is shown that the condition goo(z) > 0 for all z E U is necessary and sufficient to rewrite them in a unified manner as evolution equations at4 = L(,)4. Here L ( 8) is a linear first order differential operator on the pre-Hilbert space ( C r ( U t , C "+'), (. , . )) , where Ut C R3 is the image of the coordinate map of the spacelike hypersurface t = const, and (4,$~) = 4*Q@ d(3)2 with a suitable Hermitian n x n-matrix Q = & ( t , z ) . The total energy of the spinor field 4 with respect to Ut is then simply given by E = (+,4). In this way inequalities for the energy change rate with respect to time, &11+112 = 2 Re (4, L ( 8 , 4 ) , are obtained. As an application, the Kerr -Newman black hole is studied, yielding quantitative estimates for the energy change rate. These estimates especially confirm the energy conservation of the Weyl field and the well -known superradiance of electromagnetic waves. ui zo = c t , c the speed of light, where the hypersurfaces { t = const} are Ct n U.