Effective spacetime from multi-dimensional gravity

We study the effective spacetimes in lower dimensions that can be extracted from a multidimensional generalization of the Schwarzschild-Tangherlini spacetimes derived by Fadeev, Ivashchuk and Melnikov (Phys. Lett, A 161 (1991) 98). The higher-dimensional spacetime has D = (4 + n + m) dimensions, where n and m are the number of “internal” and “external” extra dimensions, respectively. We analyze the effective (4 + n) spacetime obtained after dimensional reduction of the m external dimensions. We find that when the m extra dimensions are compact (i) the physics in lower dimensions is independent of m and the character of the singularities in higher dimensions, and (ii) the total gravitational mass M of the effective matter distribution is less than the Schwarzshild mass. In contrast, when the m extra dimensions are large this is not so; the physics in (4 + n) does explicitly depend on m, as well as on the nature of the singularities in high dimensions, and the mass of the effective matter distribution (with the exception of wormhole-like distributions) is bigger than the Schwarzshild mass. These results may be relevant to observations for an experimental/observational test of the theory. PACS: 04.50.+h; 04.20.Cv