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We examine the effective field equations that are obtained from theaxi-dilaton gravity action with a second order Euler-Poincare term and acosmological constant in all higher dimensions. We solve these equations forfive-dimensional spacetimes possessing homogeneity and isotropy in theirthree-dimensional subspaces. For a number of interesting special cases we showthat the solutions fall into two main classes: The first class consists oftime-dependent solutions with spherical or hyperboloidal symmetry which requirecertain fine-tuning relations between the coupling constants of the model andthe cosmological constant. Solutions in the second class are locally static andprove the validity of Birkhoff's staticity theorem in the axi-dilaton gravity.We also give a special class of static solutions, among them the well-knownblack hole solutions in which the usual electric charge is superseded by anaxion charge.Comment: New formulas and references adde

Exact solutions in five-dimensional axi-dilaton gravity with Euler–Poincaré term