On the uniqueness of the ADS spacetime. (English) Zbl 1082.53040

The author proves that the \(n\)-dimensional anti-de Sitter space-time \((M,g,V)\) is the unique static solution to the vacuum Einstein equation with negative cosmological constant, provided: \(M\) is a spin manifold; \((M,g)\) is conformally compact and the conformal boundary is the sphere \(S^{n-1}\); \(V^{-2}g\) restricted to \(S^{n-1}\) is the standard metric. Moreover, it is proven that for \(n \leq 7\), the spin assumption may be removed.


53C24 Rigidity results
58Z05 Applications of global analysis to the sciences
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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