The Bach-flat and conformally Einstein equations for Siklos spacetimes

Abstract

Within the large class of Siklos spacetimes, we completely classify Bach-flat metrics, which turn out to be related to a bi-harmonicity property of the defining function. Using this classification, we tackle the conformally Einstein property and several classes of conformally Einstein Siklos metrics are then determined, including all the homogeneous examples.

Keywords

• siklos spacetimes
• bach-flat metrics
• conformally einstein metrics