Some remarks on conformal symmetries and Bartnik's splitting conjecture

TL;DR

This paper explores the geometric implications of timelike conformal Killing vector fields in globally hyperbolic spacetimes, providing insights related to Bartnik's splitting conjecture and extending previous results by Galloway and Vega.

Contribution

It offers new geometric results concerning conformal symmetries in spacetimes, complementing existing theorems on Bartnik's splitting conjecture.

Findings

Established new geometric consequences of conformal Killing vectors

Provided a complementary result to Galloway and Vega's main theorem

Enhanced understanding of spacetime splitting conditions

Abstract

Inspired by the results in a recent paper by G. Galloway and C. Vega (see arXiv:1712.00785), we investigate a number of geometric consequences of the existence of a timelike conformal Killing vector field on a globally hyperbolic spacetime with compact Cauchy hypersurfaces, especially in connection with the so-called Bartnik's splitting conjecture. In particular we give a complementary result to the main theorem in Galloway and Vega's paper.