Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-05-02
Class.Quant.Grav. 22 (2005) 3911-3922
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
9 pages, no figures, REVTeX 4; version accepted for publication in CQG
Scientific paper
10.1088/0264-9381/22/19/007
The quadrupole formula in four-dimensional Einstein gravity is a useful tool to describe gravitational wave radiation. We derive the quadrupole formula for the Kaluza-Klein (KK) modes in the Randall-Sundrum braneworld model. The quadrupole formula provides transparent representation of the exterior weak gravitational field induced by localized sources. We find that a general isolated dynamical source gives rise to the 1/r^2 correction to the leading 1/r gravitational field. We apply the formula to an evaluation of the effective energy carried by the KK modes from the viewpoint of an observer on the brane. Contrary to the ordinary gravitational waves (zero mode), the flux of the induced KK modes by the non-spherical part of the quadrupole moment vanishes at infinity and only the spherical part contributes to the flux. Since the effect of the KK modes appears in the linear order of the metric perturbations, the effective energy flux observed on the brane is not always positive, but can become negative depending on the motion of the localized sources.
Kinoshita Shunichiro
Kudoh Hideaki
Sato Katsuhiko
Sendouda Yuuiti
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