Two rival languages for curved spacetime finally get a dictionary

Two powerful but historically separate mathematical frameworks for solving Einstein's equations — Newman–Penrose and the 1+1+2 semitetrad approach — are now fully mapped onto each other. Every spin coefficient, Ricci scalar, and Weyl scalar gets a geometric translation. As a payoff, the authors use this dictionary to find necessary conditions for black hole horizons to form in a physically important class of symmetric spacetimes.