Retarded potentials and radiation in odd dimensions

Gal'Tsov, D. V.; Khlopunov, M.

doi:10.1142/9789811269776_0053

Cited by 1 publication

(2 citation statements)

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“…However, being based on the computations in the momentum space, which are irrelevant to the dimensionality of the spacetime, it does not provide us with the information about the structure of radiation field in the wave zone and the role of tail term in the formation of radiation. Recently, it has been shown that the role of tail term in the radiation can be studied in two ways: by Fourier transforming retarded Green's functions over the time coordinate [50] or by modifying the radiation definition [17,32,74,75]. In this paper, we follow the second approach.…”

Section: Jcap10(2023)019mentioning

confidence: 99%

“…In this work, we use the Rohrlich-Teitelboim approach to radiation [76][77][78] (see, also, [57,74,75,[79][80][81]), based on the Lorentz-invariant decomposition of the on-shell energymomentum tensor of retarded field, to extract the emitted part of three-dimensional scalar field. We demonstrate the presence of tail term in the radiation of non-relativistic charge moving along the fixed elliptical orbit.…”

Section: Jcap10(2023)019mentioning

confidence: 99%

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Non-local tails in radiation in odd dimensions

Khlopunov

2023

J. Cosmol. Astropart. Phys.

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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.

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