| Abstract: |
I will review the Petrov classification, an important (algebraic) classification of 4-dimensional Lorentzian manifolds, that led, among other things, to the discovery of the Kerr black hole solution in 1964. I will also discuss the Goldberg-Sachs theorem, which gives a very nice correspondence between light rays with "special" geometric properties, and "algebraically special" spacetimes in the Petrov classification. Finally, I will discuss recent attempts at generalizing the Petrov classification to higher dimensions, as well as some recent work with Marcus Werner (IPMU) which bears some relation to the Goldberg-Sachs theorem. |
