Late time tails of wave propagation in higher dimensional space-times

Cardoso, Vitor, Yoshida, Shijun, Dias, Oscar J.C. and Lemos, Jose P.S. (2003) Late time tails of wave propagation in higher dimensional space-times. Phys.Rev.D, 68 (6), [061503]. (doi:10.1103/PhysRevD.68.061503).

Abstract

We study the late-time tails appearing in the propagation of massless fields (scalar, electromagnetic, and gravitational) in the vicinities of a D-dimensional Schwarzschild black hole. We find that at late times the fields always exhibit a power-law falloff, but the power law is highly sensitive to the dimensionality of the spacetime. Accordingly, for odd D>3 we find that the field behaves as t−(2l+D−2) at late times, where l is the angular index determining the angular dependence of the field. This behavior is entirely due to D being odd; it does not depend on the presence of a black hole in the spacetime. Indeed this tail is already present in the flat space Green’s function. 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 law is entirely due to the presence of the black hole. The D=4 case is special and exhibits, as is well known, t−(2l+3) behavior. In the extra dimensional scenario for our Universe, our results are strictly correct if the extra dimensions are infinite, but also give a good description of the late-time behavior of any field if the large extra dimensions are large enough.

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Contributors

Author: Oscar J.C. Dias

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