Effect of extra dimensions in self-gravitating spherical bodies

The author initiates the study of three dimensional spherically symmetric metrics in which the size of an extra compact manifold is allowed to vary with distance. After establishing a fundamental set of equations, the author finds a few nontrivial exact solutions. In the first example uniqueness of the black hole solution is violated due to a Ricci-flatness of the internal manifold. In the second example a dense uniform star can be bound, exceeding the well known upper limit of the red shift, z = 2. Although realistic solutions are yet to be found, these solutions serve to illustrate peculiar features of higher dimensional gravity viewed from four spacetime dimensions