The GHP formalism (or Geroch–Held–Penrose formalism), also known as the compacted spin-coefficient formalism, is a technique used in the mathematics of general relativity that involves singling out a pair of null directions at each point of spacetime. It is a rewriting of the Newman–Penrose formalism which respects the covariance of Lorentz transformations preserving two null directions. This is desirable for Petrov Type D spacetimes, including black holes in general relativity, where there is a preferred pair of degenerate principal null directions but no natural additional structure to fully fix a preferred Newman–Penrose (NP) frame.