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We study the late-time tails appearing in the propagation of massless fields(scalar, electromagnetic and gravitational) in the vicinities of aD-dimensional Schwarzschild black hole. We find that at late times the fieldsalways exhibit a power-law falloff, but the power-law is highly sensitive tothe dimensionality of the spacetime. Accordingly, for odd D>3 we find that thefield behaves as t^[-(2l+D-2)] at late times, where l is the angular indexdetermining the angular dependence of the field. This behavior is entirely dueto D being odd, it does not depend on the presence of a black hole in thespacetime. Indeed this tails is already present in the flat space Green'sfunction. On the other hand, for even D>4 the field decays as t^[-(2l+3D-8)],and this time there is no contribution from the flat background. This power-lawis entirely due to the presence of the black hole. The D=4 case is special andexhibits, as is well known, the t^[-(2l+3)] behavior. In the extra dimensionalscenario for our Universe, our results are strictly correct if the extradimensions are infinite, but also give a good description of the late timebehaviour of any field if the large extra dimensions are large enough.Comment: 6 pages, 3 figures, RevTeX4. Version to appear in Rapid  Communications of Physical Review

Late-time tails of wave propagation in higher dimensional spacetimes