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1 results

  • 11 - * The Petrov classication by the spinor method

  • from Part I - Elements of differential geometry
  • Jerzy Plebanski, National Polytechnic Institute of Mexico, Andrzej Krasinski, Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences
  • Book:
    An Introduction to General Relativity and Cosmology
    Published online:
    30 May 2024
    Print publication:
    06 June 2024, pp 108-120

  • Summary

    Spinors are defined, their basic properties and relation to tensors are derived. The spinor image of the Weyl tensor is derived and it is shown that it is symmetric in all four of its spinor indices. From this, the classification of Weyl tensors equivalent to Petrov’s (by the Penrose method) is derived. The equivalence of these two approaches is proved. The third (Debever’s) method of classification of Weyl tensors is derived, and its equivalence to those of Petrov and Penrose is demonstrated. Extended hints for verifying the calculations (moved to the exercises section) are provided.