AbstractThe covariant Weyl (spins =1/2) and Maxwell (s= 1) equations in certain local charts (u, φ) of a space‐time (M, g) are considered. It is shown that the conditiong00(x)>0 for allxε u is necessary and sufficient to rewrite them in a unified manner as evolution equations δtφ = L(s)φ. HereL(s)is a linear first order differential operator on the pre—Hilbert space (C 0∞(Ut,2s+1). (…)), whereUt⊂IR3is the image of the coordinate map of the spacelike hyper‐surfacet= const, and (φ, C) = ƒUtϕ *Q d(3)xwith a suitable Hermitiann×n‐ matrixQ = Q(t,x). The total energy of the spinor field ϕ with respect toUtis then simply given byE = 〈ϕ,ϕ〉. In this way inequalities for the energy change rate with respect to time, δtϕ2= 2Re (ϕ,L(s)ϕ) 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
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