The Plebanski tensor is an order 4 tensor in general relativity constructed from the trace-free Ricci tensor. It was first defined by Jerzy Plebański in 1964.
Let formula_1 be the trace-free Ricci tensor:
formula_2
Then the Plebanski tensor is defined as
formula_3
The advantage of the Plebanski tensor is that it shares the same symmetries as the Weyl tensor. It therefore becomes possible to classify different spacetimes based on additional algebraic symmetries of the Plebanski tensor in a manner analogous to the Petrov classification.