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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.12949 |
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| _version_ | 1866914263461789696 |
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| author | Valchev, Galin S. |
| author_facet | Valchev, Galin S. |
| contents | Electrovac pp--waves in Brinkmann form provide exact Einstein--Maxwell solutions for co--propagating null radiation. Motivated by lensing or scattering, one often ``modulates'' a plane electromagnetic wave by a weak transverse envelope $1+γf(x,y)$. We show that, within the aligned null pp--wave ansatz ($A_v=0$, no $v$--dependence, $F_{xy}=0$) and enforcing the source--free Maxwell equations to $\mathcal O(γ)$, a generic profile $f(x,y)$ is incompatible with Maxwell: the transverse field $F_{ui}$ must be both divergence--free and curl--free on the transverse plane, hence $F_{ui}=\partial_iΦ$ with $Δ_\perpΦ=0$.
We give a minimal, polarization--agnostic gauge completion of the modulated potential and prove a cancellation theorem: under standard decay/regularity (or zero--mode) conditions that exclude additional harmonic transverse modes, all $\mathcal O(γ)$ dependence on $f$ drops out of $F_{ui}$ and therefore out of the electrovac source $T_{uu}$. Consequently, the electromagnetic contribution to the Brinkmann profile is universal at $\mathcal O(γ)$: the familiar cycle--averaged isotropic $r^2$ term plus an isotropic oscillatory correction at frequency $2ω$, present only for non-circular polarisation. We isolate the residual Maxwell--admissible freedom as harmonic (holomorphic) transverse data and, by Kerr--Schild linearity, superpose an arbitrary co--propagating vacuum gravitational pp--wave, relating TT--gauge strain to Brinkmann amplitudes. Modelling genuinely localised beams, therefore, requires currents, non-null components, or more general Kundt/gyraton geometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12949 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Transverse modulation in electrovac Brinkmann pp-waves: Maxwell consistency and curvature universality Valchev, Galin S. General Relativity and Quantum Cosmology Mathematical Physics Electrovac pp--waves in Brinkmann form provide exact Einstein--Maxwell solutions for co--propagating null radiation. Motivated by lensing or scattering, one often ``modulates'' a plane electromagnetic wave by a weak transverse envelope $1+γf(x,y)$. We show that, within the aligned null pp--wave ansatz ($A_v=0$, no $v$--dependence, $F_{xy}=0$) and enforcing the source--free Maxwell equations to $\mathcal O(γ)$, a generic profile $f(x,y)$ is incompatible with Maxwell: the transverse field $F_{ui}$ must be both divergence--free and curl--free on the transverse plane, hence $F_{ui}=\partial_iΦ$ with $Δ_\perpΦ=0$. We give a minimal, polarization--agnostic gauge completion of the modulated potential and prove a cancellation theorem: under standard decay/regularity (or zero--mode) conditions that exclude additional harmonic transverse modes, all $\mathcal O(γ)$ dependence on $f$ drops out of $F_{ui}$ and therefore out of the electrovac source $T_{uu}$. Consequently, the electromagnetic contribution to the Brinkmann profile is universal at $\mathcal O(γ)$: the familiar cycle--averaged isotropic $r^2$ term plus an isotropic oscillatory correction at frequency $2ω$, present only for non-circular polarisation. We isolate the residual Maxwell--admissible freedom as harmonic (holomorphic) transverse data and, by Kerr--Schild linearity, superpose an arbitrary co--propagating vacuum gravitational pp--wave, relating TT--gauge strain to Brinkmann amplitudes. Modelling genuinely localised beams, therefore, requires currents, non-null components, or more general Kundt/gyraton geometries. |
| title | Transverse modulation in electrovac Brinkmann pp-waves: Maxwell consistency and curvature universality |
| topic | General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2601.12949 |