Gravitational radiation from a binary system in odd-dimensional spacetime

Abstract

We explore possible manifestations of an odd number of extra dimensions in gravitational radiation, which are associated with violation of Huygens' principle in flat odd-dimensional spacetime. Our setup can be regarded as the limit of an infinite compactification radius in ADD model and is not viable as realistic cosmology, but it still may be useful as a simple analytically solvable model catching certain features of more realistic scenarios. The model consists of two point masses moving inside a flat three-dimensional brane, embedded in a five-dimensional Minkowski space and interacting only through a massless scalar field localized on the same brane, while gravitational radiation is emitted into the bulk. This setup avoids the difficulties associated with taking into account the gravitational stresses binding the system, which require the cubic terms in the perturbative gravitational Lagrangian, and permits to limit ourselves to linearized theory. We calculate radiation in a linearized five-dimensional gravity generalizing the Rohrlich-Teitelboim approach to extract the emitted part of the retarded gravitational field. The source term consists of a local contribution from point particles and a non-local contribution from scalar field stresses, which is calculated using the DIRE approach to post-Newtonian expansions. In the nonrelativistic limit, we find an analog of the quadrupole formula containing an integral over the history of the particles' motion preceding the retarded time. We also show that, for an observer on the brane, the radiation contains a third polarization: the breathing mode.

Non-local tails in radiation in odd dimensions

“…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.…”

“…(2.19). Also, the emitted part of the field (2.31) is given by the integral over the history of particle motion preceding the retarded time τ ≤ τ , which is a characteristic feature for all odd dimensions [17,32,74]. It is these integrals over the history of source motion that should result…”

“…Here, we took into account that the higher derivatives of particle coordinates should also be small for the particle to be non-relativistic the entire history of its motion (for detailed proof see, e.g., [17]). As a result, the integral amplitude (2.31) up to the first order in small parameters takes the form…”

“…Recently, actively developing gravitational-wave astronomy opens up new ways for the experimental study of extra dimensions (for review see, e.g., [14,15]). Extra dimensions can manifest themselves in gravitational-wave signals in the number of ways: as additional polarisations of gravitational waves [16][17][18], tower of massive highfrequency Kaluza-Klein modes of gravitational waves [16,19], additional contributions to the source of gravitational field [20][21][22][23], differences between the propagation of gravitational and counterpart electromagnetic signals [24][25][26][27], leakage of gravitational waves into extra dimensions [28][29][30][31][32], signal modifications due to the tidal charges of black holes [33,34], as well as the modifications of quasi-normal modes [35,36] and tidal deformabilities of black holes and neutron stars [37][38][39]. Also, it is worth noting here another powerful tool to probe extra dimensions -the photographs of black hole shadows [40][41][42][43].…”

Gravitational wave from extreme mass-ratio inspirals as a probe of extra dimensions

“…However, these black holes carry tidal charges, which can take negative values, unlike the electric charge of Reissner-Nordström black holes. 1 The observational consequences of tidal-charged black holes have been discussed in the literature in the context of black hole shadow and gravitational wave observations [46][47][48][49][50][51][52][53][54][55][56][57][58]. In the present context, we consider the effect of tidal charge on the EMRI waveform and check whether LISA observation can put a tighter constraint on this parameter and, consequently, on the extra dimensions.…”