Solutions of Einstein's equations with conformal Killing vector fields and initial data

Abstract

We present a survey of the research done on space-time solutions of Einstein's equations with a conformal Killing vector (CKV) and an initial data. This includes recent works of Sultana-Dyer [29,30] and Duggal [13] on a role of CKV in the study of time-dependent physically realistic black hole horizons. We also provide several references related to the use of CKV's in geometry and physics.