Filipe Nazaré | Searcharxiv

arXiv2026

Wave optical imaging of an oscillating electric dipole orbiting a black hole

We study the electromagnetic radiation and wave-optical imaging of an oscillating electric dipole orbiting a Kerr black hole. We derive the effective 4-current associated with a pointlike oscillating electric dipole in curved spacetime, and use black hole perturbation theory to compute the resulting radiation field at future null infinity, from first principles. We then develop a wave-optical imaging framework for a moving electromagnetic source in curved spacetime. We obtain images of an orbiting electric dipole, displaying relativistic beaming, gravitational lensing, and Einstein rings. We study polarization-dependent scattering by comparing the images produced by spinning dipoles with opposite helicities, finding a displacement that roughly decreases with the inverse of the radiation frequency, as expected for a beyond-geometric-optics effect. Our results provide a first-principles benchmark for beyond-geometric-optics descriptions of electromagnetic radiation in Kerr spacetime.

gr-qc↗

arXiv2026

Relativistic Elastic Response to Gravitational Waves: Explicit Solutions for a Rectangular Plate

We study the interaction between gravitational waves and elastic bodies within the framework of relativistic elasticity. Starting from the Lagrangian formulation of relativistic elasticity, we derive the linearized equations governing the response of a homogeneous and isotropic solid to a weak gravitational wave by expanding the action to quadratic order in the elastic field derivatives and to linear order in the metric perturbation. In this way, Dyson's interaction term from the effective potential approach emerges naturally from the relativistic theory. We then apply the formalism to a thin rectangular elastic plate aligned with the direction of propagation and polarization of a plus-polarized gravitational wave. For a material with vanishing Poisson ratio, the equations decouple and admit simple explicit solutions. We obtain closed-form expressions for the induced displacements and for the energy deposited on the plate by both short gravitational wave bursts and continuous harmonic waves. Finally, we compute the gravitational wave emission generated by the oscillating plate itself under continuous harmonic excitation. These results provide a fully relativistic derivation of the elastic response to gravitational waves together with explicit solvable examples relevant to resonant gravitational wave detectors.

gr-qc↗