Quartic equations and classification of Riemann tensors in general relativity
Abstract
For spacetimes in general relativity, the Petrov classification of the Weyl conformai curvature and the Plebański or Segre classification of the Ricci tensor each depend on the properties of the roots of quartic equations. The coefficients in these quartic equations are in general complicated functions of the spacetime coordinates. We review the general theory of quartic equations, and discuss algorithms for determining the existence and values of multiple roots. We consider practical implementation of an algorithm and the consequent Petrov classification. Tests of programs embodying this algorithm, using the computer algebra system CLASSI based on SHEEP, are reported.
 Publication:

General Relativity and Gravitation
 Pub Date:
 September 1991
 DOI:
 10.1007/BF00756865
 Bibcode:
 1991GReGr..23.1023A