Homothetic Killing Vectors in Expanding HH-Spaces with Lambda

TL;DR

This paper investigates conformal Killing vectors in expanding hyperheavenly spaces with a cosmological constant, showing they reduce to homothetic or isometric vectors, and classifies these vectors with detailed analysis of specific spacetime types.

Contribution

It provides a reduction of conformal Killing equations to a master equation and offers a classification of homothetic and isometric vectors in these spaces.

Findings

Conformal Killing vectors reduce to homothetic or isometric vectors.

A master equation for Killing vectors is derived.

Explicit metrics with isometric Killing vectors are identified for certain spacetime types.

Abstract

Conformal Killing equations and their integrability conditions for expanding hyperheavenly spaces with Lambda in spinorial formalism are studied. It is shown that any conformal Killing vector reduces to homothetic or isometric Killing vector. Reduction of respective Killing equation to one master equation is presented. Classification of homothetic and isometric Killing vectors is given. Type [D]x[any] is analysed in details and some expanding HH complex metrics of types [III, N]x[III, N] with Lambda admitting isometric Killing vectors are found.