Any good references of Petrov Classification?

yicong2011
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Is there any good references of Petrov Classification?

Thank you.
 
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If I were to go to the nearest college library, I'd search for the 2 volumes of Penrose and Rindler's book on spinors and twistors. If I didn't find the desired treatment, then I would look in all the books Moshe Carmeli wrote.
 
A readable account appears in "Introduction to General Relativity" from Ryder. Personally, I learned it from Relativity: An Introduction to Special and General Relativity by Stephani.
 
I tried several sources to learn about this, and I still don't understand it thoroughly at all. The source that worked best for me was "Survey of gravitational radiation theory," F.A.E. Pirani, in Recent Developments in General Relativity, Pergamon, 1962, p. 89. You can presumably find it if you have access to a large university library. It's very concrete and down to earth, and it relates the ideas to their counterparts in E&M.
 
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In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
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