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.
The GHP formalism notices that given a spin-frame
The magnitude of this transformation is a boost, and the phase tells one how much to rotate.
One then defines derivative operators which take tensors under these transformations to tensors.
This simplifies many NP equations, and allows one to define scalars on 2-surfaces in a natural way.
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