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

Abstract

We develop an algebraic procedure to rotate a general Newman-Penrose tetrad in a Petrov type I spacetime into a frame with Weyl scalars $\hat{I}{¨}_1$ and $\hat{I}{¨}_3$ 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 $\hat{I}{¨}_1$ and $\hat{I}{¨}_3$ to zero makes apparent the superposition of a Coulomb-type effect $\hat{I}{¨}_2$ with transverse degrees of freedom $\hat{I}{¨}_0$ and $\hat{I}{¨}_4$.

10 pages, submitted to Classical Quantum Gravity