Geometric Interpretation of the Mixed Invariants of the Riemann Spinor

Mixed invariants are used to classify the Riemann spinor in the case of Einstein-Maxwell fields and perfect fluids. In the Einstein-Maxwell case these mixed invariants provide information as to the relative orientation of the gravitational and electromagnetic principal null directions. Consideration of the perfect fluid case leads to some results about the behaviour of the Bel-Robinson tensor regarded as a quartic form on unit timelike vectors.Comment: 31 pages, AMS-LaTe

A new algorithm for the Petrov classification of the Weyl tensor

A new algorithm for the Petrov classification of the Weyl tensor is introduced. It is similar to the Letniowski-McLenaghan algorithm [1] when someof the &yen;\u27s are zero, but offers a completely new approach when all of the &yen;\u27s are nonzero. In all cases, new code in Maple has been implemented.<br /