Spinors, Jets, and the Einstein Equations

Details Spinors, Jets, and the Einstein Equations Spinors, Jets, and the Einstein Equations

1995-08-03

arxiv.org/abs/gr-qc/9508005v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

to appear in the proceedings of the Sixth Canadian Conference on General Relativity and Relativistic Astrophysics, 13 pages, u

Scientific paper

Many important features of a field theory, {\it e.g.}, conserved currents, symplectic structures, energy-momentum tensors, {\it 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 of non-existence of ``local observables'' for vacuum spacetimes and a uniqueness theorem for the gravitational symplectic structure.

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