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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.

MSC:

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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References:

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