Abstract
The initial-value problem of general relativity is treated in the case where the external sources are electromagnetic or neutrino fields. Taking into account the initial conditions that must be satisfied by these fields, we show that the resulting equations in each case form a quasilinear elliptic system of a type that has been treated extensively in previous work. We also treat the initial-value problem of the scalar-tensor theory of gravitation. Throughout this work we use first-order canonical gravitational variables. The principal mathematical tools are conformal transformations and a covariant decomposition of symmetric tensors.
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