Ultrastatic spacetimes

TL;DR

This paper explores the properties of ultrastatic spacetimes, characterizing when a spacetime can be ultrastatic or conformally ultrastatic, with implications for calculations in conformally static backgrounds.

Contribution

It provides a detailed analysis of conditions under which spacetimes can be ultrastatic or conformally ultrastatic, highlighting their geometric structures.

Findings

Ultrastatic spacetimes are products with Minkowskian factors.

Conformally ultrastatic spacetimes have spatial sections conformal to product spaces.

The paper clarifies the geometric criteria for ultrastatic and conformally ultrastatic spacetimes.

Abstract

Several calculations in conformally static spacetimes rely on the introduction of an ultrastatic background. I describe the general properties of ultrastatic spacetimes, and then focus on the problem of whether a given spacetime can be ultrastatic, or conformally ultrastatic, in more than one way. I show that the first possibility arises iff the spacetime is a product containing a Minkowskian factor, and that the second arises iff the spatial sections are conformal to a product space.