Electromagnetic, gravitational wave, and static gravitational transmission through throat spacetimes: a constraint-wave asymmetry

Abstract

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 Schr\"odinger problem with centrifugal barrier $V_\ell^{(\mathrm{EM})}=\ell(\ell+1)/(\sigma^2+r_0^2)$ peaked at the throat. For the lowest physical EM mode ($\ell=1$), frequencies below the barrier-top frequency $\omega_{\max}=\sqrt{2}/r_0$ are strongly suppressed by sub-barrier tunnelling. Gravitational wave perturbations ($\ell\ge 2$) see a qualitatively similar barrier and are likewise strongly suppressed below their respective barrier-top frequencies. By contrast, the static gravitational monopole ($\ell=0$), governed by the linearised Einstein equations on the same background, satisfies the source-free conservation law $(a^2\Phi')'=0$ with no potential barrier, yielding the exact solution $\Phi\propto\arctan(\sigma/r_0)$. 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 --- strong sub-barrier suppression for all propagating radiation ($\ell\ge 1$) versus polynomial attenuation for the static monopole ($\ell=0$) --- 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.