Uniqueness of the ADS spacetime in any dimensions
نویسنده
چکیده
In Einstein’s theory of general relativity with a negative cosmological constant Λ, a vacuum spacetime is a solution to the equation Rab = Λgab and the lowest-energy solution is the anti-de Sitter spacetime. Moreover it was proved by Bocher-GibbonsHorowitz [BGH84] in 3+1 dimensions that the anti-de Sitter spacetime is the unique static, asymptotically anti-de Sitter vacuum. To give the precise statement of their theorem, let us first recall that an (n + 1) dimensional static spacetime (N, g) has the form
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