Holonomy and projective symmetry in space-times

TL;DR

This paper investigates the relationship between holonomy types and the existence of proper projective vector fields in space-times, establishing non-existence for certain types and confirming existence for others, along with local uniqueness results.

Contribution

It classifies holonomy types in space-times and determines the conditions under which proper projective vector fields can or cannot exist, providing new theoretical insights.

Findings

Proper projective vector fields do not exist for certain holonomy types.

Existence of proper projective vector fields is confirmed for remaining holonomy types.

A local uniqueness theorem is established for all but the most general holonomy type.

Abstract

It is shown using a space-time curvature classification and decomposition that for certain holonomy types of a space-time, proper projective vector fields cannot exist. Existence is confirmed, by example, for the remaining holonomy types. In all except the most general holonomy type, a local uniqueness theorem for proper projective symmetry is established.