Einstein equations and conformal structure: Existence of anti-de Sitter-type space-times. (English) Zbl 0840.53055

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 O. Guès of 1990.


53Z05 Applications of differential geometry to physics
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
53A30 Conformal differential geometry (MSC2010)
83C15 Exact solutions to problems in general relativity and gravitational theory
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