Bound states in the continuum of gravitational waves
Abstract
Bound states in the continuum (BICs) are ubiquitous wave phenomena, but have not yet been demonstrated for gravitational waves (GWs). Here, in-plane periodic perturbations, exponentially localized at the plane z = 0, are shown to lead to distributional surface energy tensors at this plane and to be regular vacuum solutions (Tμν = 0) of the linearized Einstein field equations outside of it. These are achieved by explicitly calculating the Ricci tensor components and the Ricci scalar from the metric perturbation tensor. To fulfill each vacuum solution (Rσν(+, ×) = 0 and R(+, ×) = 0), different surface polariton-like dispersions are required. These bound perturbations decay exponentially to a flat metric (hBIC(+,×) ∝ e− kz |z|), and each localized metric has a correspondence to a different planar GW polarization (+,×). The Lorenz gauge-fulfilling solutions exist at the Γ point in momentum space, dwelling within the continuum of wavevectors of propagating GWs. The strains in the unit cell of the periodic perturbations have opposite parities relative to the corresponding planar GWs under a C2 in-plane rotation, making them incompatible by symmetry with their propagating counterpart, indicating localization via symmetry protection.
Versions
Related
- Doublon bound states in the continuum through giant atoms
- Topologically protected bound states in the continuum in the Su-Schrieffer-Heeger chain
- Topological Leading Angular Structure around Bound States in the Continuum
- Acoustic scattering singularities via quasi-Bound states in the continuum
- Fourier modal method for perturbation analysis of bound states in the continuum
BibTeX
@misc{berte2026bound,
title = {{Bound states in the continuum of gravitational waves}},
author = {Rodrigo Berté},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10620},
eprint = {2609.10620},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10620},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Bound states in the continuum of gravitational waves
AU - Rodrigo Berté
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.10620
UR - https://arxiv.org/abs/2609.10620
AB - Bound states in the continuum (BICs) are ubiquitous wave phenomena, but have not yet been demonstrated for gravitational waves (GWs). Here, in-plane periodic perturbations, exponentially localized at the plane z = 0, are shown to lead to distributional surface energy tensors at this plane and to be regular vacuum solutions (T_μν = 0) of the linearized Einstein field equations outside of it. These are achieved by explicitly calculating the Ricci tensor components and the Ricci scalar from the metric perturbation tensor. To fulfill each vacuum solution (R_σν_(+, ×) = 0 and R__(+, ×) = 0), different surface polariton-like dispersions are required. These bound perturbations decay exponentially to a flat metric (h_BIC_(+,×) ∝ e^− k_z |z|), and each localized metric has a correspondence to a different planar GW polarization (+,×). The Lorenz gauge-fulfilling solutions exist at the Γ point in momentum space, dwelling within the continuum of wavevectors of propagating GWs. The strains in the unit cell of the periodic perturbations have opposite parities relative to the corresponding planar GWs under a C_2 in-plane rotation, making them incompatible by symmetry with their propagating counterpart, indicating localization via symmetry protection.
ER -