Abstract
We examine the Kaluza–Klein (KK) dimensional reduction from higher dimensional space-time and the properties of the resultant Bergmann–Wagoner general action of scalar–tensor theories. With the analysis of the perturbations, we also investigate the stability of the anti-de Sitter (AdS) space-time in the (D ∈ 𝒩)-dimensional Einstein gravity with the negative cosmological constant. Furthermore, we derive the conditions for the dimensional reduction to successfully be executed and present the KK compactification mechanism.
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