MULTIDIMENSIONAL GRAVITY AND NO-BOUNDARY CONDITION

In this work 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 in a four-dimensional spacetime and an extra (D-4)-dimensional space, with classical 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 Einsteinian theory which describes the dynamics of the four-dimensional spacetime and the matter fields. The exponential action of the considered D-dimensional classical solutions provides then a semiclassical approximation to the wave functions of this effective theory. When we adopt a no-boundary condition, this action turns out to contain, in addition, implicit information about the local behaviour of the semiclassical wave functions of the multidimensional model in the superspace region associated to the effective four-dimensional theory.