Transverse frames for Petrov type I spacetimes: a general algebraic procedure

We develop an algebraic procedure to rotate a general Newman-Penrose tetrad in a Petrov type I spacetime into a frame with Weyl scalars ${\mathrm{\Psi }}_1$ and ${\mathrm{\Psi }}_3$ equal to zero, assuming that initially all the Weyl scalars are non vanishing. The new frame highlights the physical properties of the spacetime. In particular, in a Petrov Type I spacetime, setting ${\mathrm{\Psi }}_1$ and ${\mathrm{\Psi }}_3$ to zero makes apparent the superposition of a Coulomb-type effect ${\mathrm{\Psi }}_2$ with transverse degrees of freedom ${\mathrm{\Psi }}_0$ and ${\mathrm{\Psi }}_4$.