Non-expanding horizons: multipoles and the symmetry group

It is well-known that blackhole and cosmological horizons in equilibrium situations are well-modeled by non expanding horizons (NEHs) [1–3]. In the first part of the paper we introduce multipole moments to characterize their geometry, removing the restriction to axisymmetric situations made in the existing literature [4]. We then show that the symmetry group $$ \mathfrak{G} $$ G of NEHs is a 1-dimensional extension of the BMS group $$ \mathfrak{B} $$ B . These symmetries are used in a companion paper [5] to define charges and fluxes on NEHs, as well as perturbed NEHs. They have physically attractive properties. Finally, it is generally not appreciated that $$ \mathcal{I} $$ I ±of asymptotically flat space-times are NEHs in the conformally completed space-time. Forthcoming papers will (i) show that $$ \mathcal{I} $$ I ± have a small additional structure that reduces $$ \mathfrak{G} $$ G to the BMS group $$ \mathfrak{B} $$ B , and the BMS charges and fluxes can be recovered from the NEH framework; and, (ii) develop gravitational wave tomography for the late stage of compact binary coalescences: reading-off the dynamics of perturbed NEHs in the strong field regime (via evolution of their multipoles), from the waveform at $$ \mathcal{I} $$ I +.

Conditions for a pure toroidal dipole source

Recently, the physical significance of dynamic toroidal multipoles in the context of electrodynamics has been put under discussion. Indeed, the latter can be shown to arise simply from a Taylor series of the exact source (Cartesian) multipole moments. The split into elementary and toroidal parts was demonstrated to lead to an unphysical result were forbidden components of the momentum transform of the current could radiate into free space. In this contribution, we elaborate the conditions that a current distribution must necessarily satisfy to be considered a ‘pure’ toroidal dipole source. We demonstrate for the first time that symmetry prevents such current distribution to radiate as an elementary electric dipole moment, without leading to an unphysical result. Thus, while both elementary electric dipole and toroidal dipoles are indistinguishable outside the source, they display topologically distinct characteristics within the smallest spherical surface enclosing the source itself and have different physical origin. Based on our results, a pure ‘toroidal’ source can be designed. We believe the outcome of our investigations will help clarify further the formal meaning of the toroidal multipoles.

Polarization-independent anapole response of a trimer-based dielectric metasurface

The phenomenon of anapole has attracted considerable attention in the field of metamaterials as a possible realization of radiationless objects. We comprehensively study this phenomenon in the cluster-based systems of dielectric particles by considering conditions of anapole manifestation in both single trimers of disk-shaped particles and metamaterial composed on such trimers. Our analytical approach is based on the multipole decomposition method and the secondary multipole decomposition technique. They allow us to associate the anapole with the multipole moments of the trimer and the separate multipole moments of its constitutive particles. The manifestation of anapole in a two-dimensional metamaterial (metasurface) is confirmed by checking the resonant states in the reflected field as well as from the electromagnetic near-field patterns obtained from the full-wave numerical simulation. It is demonstrated that the anapole excitation in trimers results in the polarization-independent suppression of reflection with the resonant enhancement of local electromagnetic fields in the metasurface. Finally, experimental verification of the theoretical results is presented and discussed.

The Radiative Δ(1600) → γN Decay in the Light-Cone QCD Sum Rules

Within the framework of the light-cone QCD sum rules method (LCSR’s), the radiative Δ(1600)→γN decay is studied. In particular, the magnetic dipole moment GM1(0) and the electric quadrupole moment GE1(0) are estimated. We also calculate the ratio REM=−GE1(0)GM1(0) and the decay rate. The predicted multipole moments and the decay rate strongly agree with the existing experimental results as well as with the other available phenomenological approaches.