No-boundary condition in multidimensional gravity

Abstract

We consider D-dimensional Lovelock models whose matter action does not depend on the time derivatives of the metric, and which admit classical solutions in which the spacetime splits into a four-dimensional spacetime and an extra (D − 4)-dimensional space, with matter fields independent of the extra D − 4 coordinates. Freezing the extra degrees of freedom of the metric at the values they take in such classical solutions, we obtain an effective four-dimensional Einsteinian theory. The exponential action of the no-boundary D-dimensional classical solutions provides then a semiclassical approximation to the wave functions of this effective theory, and contains implicit information about the local behaviour of the semiclassical wave functions of the multidimensional model.