On geometry of congruences of null strings in 4-dimensional complex and real pseudo-Riemannian spaces

TL;DR

This paper investigates the geometric properties of congruences of null strings in 4-dimensional complex and real pseudo-Riemannian spaces, analyzing their relations with spacetime algebraic classifications.

Contribution

It provides a detailed analysis of null string congruences and their connections to Petrov-Penrose types and Ricci tensor classifications in 4D spaces.

Findings

Relations between null string congruences and Petrov-Penrose types established

Characterization of null string properties in various algebraic spacetime types

Insights into the geometry of totally null, totally geodesic surfaces in 4D spaces

Abstract

4-dimensional spaces equipped with 2-dimensional (complex holomorphic or real smooth) completely integrable distributions are considered. The integral manifolds of such distributions are totally null and totally geodesics 2-dimensional surfaces which are called the null strings. Properties of congruences (foliations) of such 2-surfaces are studied. Some relations between properties of congruences of null strings, Petrov-Penrose type of SD Weyl spinor and algebraic types of the traceless Ricci tensor are analyzed.