Generalization of the Geroch-Held-Penrose formalism to higher dimensions

TL;DR

This paper extends the Geroch-Held-Penrose formalism to higher-dimensional spacetimes, simplifying the equations involved and enabling new analysis of algebraically special p-form fields.

Contribution

The paper introduces a higher-dimensional generalization of the Geroch-Held-Penrose formalism, making the study of such spacetimes more tractable and revealing new properties of p-form fields.

Findings

Simpler equations compared to previous higher-dimensional formalisms

Analysis of p-form test field dynamics in higher dimensions

Proofs of properties of algebraically special p-form fields

Abstract

Geroch, Held and Penrose invented a formalism for studying spacetimes admitting one or two preferred null directions. This approach is very useful for studying algebraically special spacetimes and their perturbations. In the present paper, the formalism is generalized to higher-dimensional spacetimes. This new formalism leads to equations that are considerably simpler than those of the higher-dimensional Newman-Penrose formalism employed previously. The dynamics of p-form test fields is analyzed using the new formalism and some results concerning algebraically special p-form fields are proved.