Electromagnetic, gravitational wave, and static gravitational transmission through throat spacetimes: a constraint-wave asymmetry
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arXiv
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| Natura: | Preprint |
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2026
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| _version_ | 1866918462697242624 |
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| author | Riley, Jeff |
| author_facet | Riley, Jeff |
| contents | 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 $V_\ell^{(\mathrm{EM})}=\ell(\ell+1)/(σ^2+r_0^2)$ peaked at the throat. For the lowest physical EM mode ($\ell=1$), frequencies below the barrier-top frequency $ω_{\max}=\sqrt{2}/r_0$ 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 $(a^2Φ')'=0$ with no potential barrier, yielding the exact solution $Φ\propto\arctan(σ/r_0)$. 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\emdash strong sub-barrier suppression for all propagating radiation ($\ell\ge 1$) versus polynomial attenuation for the static monopole ($\ell=0$)\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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14238 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Electromagnetic, gravitational wave, and static gravitational transmission through throat spacetimes: a constraint-wave asymmetry Riley, Jeff General Relativity and Quantum Cosmology High Energy Physics - Theory 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 $V_\ell^{(\mathrm{EM})}=\ell(\ell+1)/(σ^2+r_0^2)$ peaked at the throat. For the lowest physical EM mode ($\ell=1$), frequencies below the barrier-top frequency $ω_{\max}=\sqrt{2}/r_0$ 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 $(a^2Φ')'=0$ with no potential barrier, yielding the exact solution $Φ\propto\arctan(σ/r_0)$. 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\emdash strong sub-barrier suppression for all propagating radiation ($\ell\ge 1$) versus polynomial attenuation for the static monopole ($\ell=0$)\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. |
| title | Electromagnetic, gravitational wave, and static gravitational transmission through throat spacetimes: a constraint-wave asymmetry |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.14238 |