New examples of static spacetimes admitting a unique standard decomposition
- 55 Downloads
In this paper we introduce a new general approach for the study of spacetimes admitting a standard static splitting. This approach allows us to give an alternative proof for the uniqueness of splitting in the spatially closed case to the first study made by Sánchez–Senovilla and later by Aledo–Romero–Rubio. However, our technique also allows us to obtain new uniqueness results for standard static models with complete (non necessarily compact) spacelike bases under some mild hypothesis, including some restrictions on the sectional curvature of such bases.
KeywordsStandard static spacetime Standard static splitting Global Killing vector field Maximal hypersurface
Mathematics Subject Classification53C50 53C80 83C20
- 13.Kazdan, J.L.: Some applications of partial differential equations to problems in geometry. J.S. Kazdan (1983)Google Scholar
- 16.Sachs, R.K., Wu, H.H.: General Relativity for Mathematicians. Springer, New York (1977). https://doi.org/10.1007/978-1-4612-9903-5