Killing Vector Fields of Standard Static Space-times

TL;DR

This paper investigates the properties of Killing vector fields in standard static space-times, deriving conditions for their existence and characterizing them in cases with compact Riemannian components.

Contribution

It provides new equations and characterizations for Killing vector fields specifically in standard static space-times, expanding understanding of their geometric structure.

Findings

Derived equations for Killing vector fields on static space-times

Characterized Killing vector fields with compact Riemannian parts

Enhanced understanding of symmetries in static space-times

Abstract

We consider Killing vector fields on standard static space-times and obtain equations for a vector field on a standard static space-time to be Killing. We also provide a characterization of Killing vector fields on standard static space-times with compact Riemannian parts.