Gradient conformal vector fields and their applications in vacuum static spaces

Abstract

The purpose of this work is to study the conformal geometry of vacuum static spaces with a constant scalar curvature, which corresponds to an interesting generalization of the critical point of the equation. We prove that a vacuum static space admitting a non-trivial gradient conformal vector field is isometric to a Euclidean space or to a warped products

Keywords

• vacuum static spaces
• closed conformal vector field
• gradient conformal vector field
• static space-time
• perfect fluid

References

1. [1] Ali, A., Alshehri, N., Mofarreh, F., and Li, Y., Geometry of gradient Einstein harmonic solitons in sequential warped products manifolds, Eur. Phys. J. Plus, 139 (4), 1–8, 2024.