2003/07/31 by Vitor Cardoso, Vítor Cardoso, Shijun Yoshida +4
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Black hole (networking) #Classical mechanics #Field (mathematics) #Massless particle #Mathematical physics #Physics #Power law #Pulsars and Gravitational Waves Research #Quantum mechanics #Scalar field #Schwarzschild radius #Spacetime #Theoretical physics #astro-ph #gr-qc #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.68.061503
published as Phys.Rev. D68 (2003) 061503 · 6 pages, 3 figures, RevTeX4. Version to appear in Rapid Communications of Physical Review D
arxiv created 2003/08/27 · openalex publication_date 2003/09/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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^\ensuremath-(2l+D\ensuremath-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^\ensuremath-(2l+3D\ensuremath-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^\ensuremath-(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.