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Details for PetrovType



The command PetrovType uses the algorithm of M. A. Acvevedo, M. M. Enciso-Aguilar, J. Lopez-Bonilla, M. A. Acvevedo, Petrov classification of the conformal tensor, Electronic Journal of Theoretical Physics, Vol. 9, (2006), 79-82 to determine the Petrov type. The algorithm depends upon certain invariants calculated from the Newman Penrose Weyl scalars Ψ0,Ψ1,Ψ2,Ψ3,Ψ4. These invariants are:



G2=Ψ02+Ψ0Ψ42 Ψ1Ψ3






 If I3=27 J2 then λ is determined by λ2=13I and λ3=J and

 Mr=Gr+λΨr , r=0,1,2,3,4

 L=G2+2 G5+3 λΨ2


The algorithm is as follows:

Step 1. If Ψ0=Ψ1=Ψ2=Ψ3=Ψ4=0, then the Petrov type is O.

Step 2. Otherwise, if G0=G1=G2=G3=G4=0, then the Petrov type is N.

Step 3. Otherwise, if I=J=0, then the Petrov type is III.

Step 4. Otherwise, if I327 J2, then the Petrov type is I.

Step 5. If I3=27 J2 and Mr=0 for r=0,1,2,3,4 and G2+2 G5+3 λΨ2=0, then the Petrov type is D.

Step 6. Otherwise, the Petrov type is II.