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arXiv · 2605.30255

A complete correspondence between the Newman-Penrose and 1+1+2 formalisms

Abbas M Sherif·Peter K S Dunsby
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Abstract

We establish a 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. In addition, we provide some discussions on the correspondence between the gauge structures of the formalisms. 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 a simple demonstration, we use this mapping to derive inequalities on the Newman-Penrose scalars and the cosmological constant, which constrains the existence of future outer trapping horizons in spacetimes exhibiting local rotational symmetry.

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Abbas M Sherif, Peter K S Dunsby. 2026-05-28. A complete correspondence between the Newman-Penrose and 1+1+2 formalisms. https://arxiv.org/abs/2605.30255

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