Celebratio Mathematica — Choquet-Bruhat

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Y. Choquet-Bruhat and A. H. Taub: “High-frequency, self-gravitating, charged scalar fields,” Gen. Relativity Gravitation 8 : 8 (1977), pp. 561–571. MR 471867 article

In this paper we shall apply the Wentzel–Kramers–Brillouin (WKB) method of expansion (the two-timing method) discussed in [Choquet-Bruhat 1969] to the equations governing the behavior of a charged scalar field \( \psi \), the vector potential \( A_{\mu} \) of an electromagnetic field that satisfies the Maxwell equations with a current vector derived from \( \psi \), and the metric tensor \( g_{\mu\nu} \) that satisfies the Einstein field equations with a stress energy tensor \( T_{\mu\nu} \) due to the electromagnetic and scalar fields. This method, in contrast to the averaged Lagrangian method given in [MacCallum and Taub 1973], allows one to determine propagation equations for various functions as well as equations involving values of various variables averaged over a period of the perturbations that are introduced.