2026/04/30 by Jeff Riley
#gr-qc #hep-th
paper · pdf · doi:10.1103/9xyc-f581
We compute the transmission properties of electromagnetic (EM), gravitational wave (GW), and static gravitational perturbations through geometric throats in spherically symmetric spacetimes. On the ultrastatic Ellis-Bronnikov background, decomposition of the four-dimensional Maxwell equations into vector spherical harmonics yields an effective Schrödinger problem with centrifugal barrier V_ℓ(EM)=ℓ(ℓ+1)/(σ2+r02) peaked at the throat. For the lowest physical EM mode (ℓ=1), frequencies below the barrier-top frequency ωmax=√(2)/r0 are strongly suppressed by sub-barrier tunnelling. Gravitational wave perturbations (ℓ≥ 2) see a qualitatively similar barrier and are likewise strongly suppressed below their respective barrier-top frequencies. By contrast, the static gravitational monopole (ℓ=0), governed by the linearised Einstein equations on the same background, satisfies the source-free conservation law (a2Φ')'=0 with no potential barrier, yielding the exact solution Φ∝\arctan(σ/r0). We extend these results to a one-parameter family of throat geometries with varying profile shapes, and to a reflected-Schwarzschild (Damour-Solodukhin-type) wormhole, demonstrating that the qualitative asymmetry\emdash strong sub-barrier suppression for all propagating radiation (ℓ≥ 1) versus polynomial attenuation for the static monopole (ℓ=0)\emdash is universal for static, spherically symmetric throats. Numerov integration, WKB estimates, and exact analytical solutions are compared throughout. The results establish a structural constraint-wave asymmetry arising from the multipole decomposition of the field equations, independent of the matter content sourcing the geometry, on a fixed background.