Kaluza-Klein reduction and Bergmann-Wagoner bi-scalar general action of   scalar-tensor gravity
  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 $D\in\mathcal{N}$-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. 
Kazuharu Bamba, Davood Momeni and Ratbay Myrzakulov
hep-th astro-ph.CO gr-qc