# Complete classification of second-order symmetric spacetimes - General Relativity and Quantum Cosmology

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Abstract: As a difference with the positive-definite Riemannian case, in the Lorentziancase there exists proper second-order symmetric spacetimes, i.e., those withvanishing second covariant derivative of the Riemannian tensor$R {\lambda\mu u ho;\alpha;\beta}=0$ which are not locally symmetric$R {\lambda\mu u ho;\alpha} eq 0$. In fact, they lie in the class ofBrinkmann metrics, and include some known plane waves. Our purpose is toclassify these spacetimes in the 4 dimensional case.

Author: ** O F Blanco, M Sánchez, J M M Senovilla**

Source: https://arxiv.org/