Einstein equations and conformal structure: Existence of anti-de Sitter-type space-times
The author develops and discusses in detail the conformal structure of space-time and, in particular, of the Einstein equations. By conformal extension, a space-time can aquire a boundary, so that asymptotic conditions become boundary conditions. Cauchy's problem to Einstein's equations is treated as an initial and boundary value problem. The author proves a theorem of existence and uniqueness of a global solution which he calls of ``anti-de Sitter type'' because of some likeness to the anti-de Sitter space-time. This type is asymptotically simple and has a positive cosmological constant. The analytical tools come from a paper of \textit{O. Guès} of 1990.
scientific article; zbMATH DE number 816010
scientific article