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Spinors, Jets, And The Einstein Equations, Charles G. Torre
Spinors, Jets, And The Einstein Equations, Charles G. Torre
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Many important features of a field theory, e.g., conserved currents, symplectic structures, energy-momentum tensors, etc., arise as tensors locally constructed from the fields and their derivatives. Such tensors are naturally defined as geometric objects on the jet space of solutions to the field equations. Modern results from the calculus on jet bundles can be combined with a powerful spinor parametrization of the jet space of Einstein metrics to unravel basic features of the Einstein equations. These techniques have been applied to computation of generalized symmetries and “characteristic cohomology” of the Einstein equations, and lead to results such as a proof …