The N--P and 1+1+2 correspondence
Abstract
In this letter, we establish a complete correspondence between the Newman--Penrose and 1+1+2 semitetrad covariant formalisms by expressing all Newman--Penrose spin coefficients, Ricci scalars, and Weyl scalars in terms of the scalar, vector, and tensor variables of the 1+1+2 decomposition. This provides a direct dictionary between two widely used approaches to general relativity and gives a geometrical interpretation of Newman--Penrose quantities in terms of covariantly defined 1+1+2 variables. As an application, we derive necessary conditions for the existence of future outer trapping horizons in locally rotationally symmetric class II spacetimes, expressed in terms of the Ricci and Weyl Newman--Penrose scalars and the cosmological constant.
Comments: 8 pages, 2-column format, no figure, comments welcome
Cite
@article{arxiv.2605.30255,
title = {The N--P and 1+1+2 correspondence},
author = {Abbas M Sherif and Peter K S Dunsby},
journal= {arXiv preprint arXiv:2605.30255},
year = {2026}
}