Non-local tails in radiation in odd dimensions

Abstract

Huygens principle violation in a spacetime of odd dimensions leads to the fact that the retarded massless fields of localised sources depend on their history of motion preceding the retarded time. This non-local character of retarded fields should result into the formation of tail signals in the radiation of localised sources. In particular, in gravity theories with odd number of extra spacetime dimensions the gravitational radiation of binary systems should contain the tail terms. In this work, we demonstrate the presence of tail signal in radiation within a simple model of scalar field interacting with the point charge moving on elliptical orbit in three dimensions. We find that the tail term results into the characteristic dependence of radiation power of the charge on time. In particular, its extremum points do not correspond to the moments when the charge passes the pericenter and apocenter of the orbit, in contrast with the four-dimensional theory. We obtain the formulae for the shifts of radiation power extremum points up to the contributions quadratic in the orbital eccentricity. We also compute the spectral distribution of radiation power of the charge. We find that in three dimensions the charge on elliptical orbit radiates into the lower harmonics of the spectrum, compared to the four-dimensional theory. We conjecture that in higher dimensions the character of spectral distributions is opposite - the charge mainly radiates into the higher harmonics of the spectrum.