The asymptotic behavior of Lorentz-violating photon fields
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912265291169792 |
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| author | Xiao, Zhi Wang, Hao |
| author_facet | Xiao, Zhi Wang, Hao |
| contents | In this work, we derive the Newman-Penrose formalism of Maxwell's equations using two approaches: differential forms and intrinsic derivatives. Denoting $(k_{AF})^μ$ as $k^μ$, with $k^μ=(k^t,k^r,0,0)$ in spherically symmetric spacetimes, we show that the expansion in $r^{-1}$ fails to produce consistent, closed solutions due to the inability to separate Lorentz-violating (LV) phase factors, as the Lorentz-invariant (LI) null tetrad does not adapt to the LV wavefront. Moreover, with exact formal solutions, we demonstrate that the expansion is nonperturbative in the LV parameter $k^2\equiv k^t-k^r$. For $r\gg1/k^2$, higher powers of $k^2$ dominate over lower powers, as the latter decay more rapidly with increasing $r$. Although the Coulomb mode $ϕ_1\sim\mathcal{O}(\ln{r}/r^2)$ deviates from the LI expectation $\mathcal{O}(r^{-2})$ due to LV corrections, the leading outgoing radiation mode remains unaffected, i.e., $ϕ_2\sim\mathcal{O}(r^{-1})$. Given the constraint $|k_{AF}|\le10^{-44}$GeV \cite{CMBLV-N}, the three complex scalars $ϕ_a$ ($a=0,1,2$) still obey the peeling theorem: $ϕ_a\sim\mathcal{O}(r^{(a-3)}),~a=0,1,2$ for large, finite distances. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04975 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The asymptotic behavior of Lorentz-violating photon fields Xiao, Zhi Wang, Hao High Energy Physics - Phenomenology General Relativity and Quantum Cosmology In this work, we derive the Newman-Penrose formalism of Maxwell's equations using two approaches: differential forms and intrinsic derivatives. Denoting $(k_{AF})^μ$ as $k^μ$, with $k^μ=(k^t,k^r,0,0)$ in spherically symmetric spacetimes, we show that the expansion in $r^{-1}$ fails to produce consistent, closed solutions due to the inability to separate Lorentz-violating (LV) phase factors, as the Lorentz-invariant (LI) null tetrad does not adapt to the LV wavefront. Moreover, with exact formal solutions, we demonstrate that the expansion is nonperturbative in the LV parameter $k^2\equiv k^t-k^r$. For $r\gg1/k^2$, higher powers of $k^2$ dominate over lower powers, as the latter decay more rapidly with increasing $r$. Although the Coulomb mode $ϕ_1\sim\mathcal{O}(\ln{r}/r^2)$ deviates from the LI expectation $\mathcal{O}(r^{-2})$ due to LV corrections, the leading outgoing radiation mode remains unaffected, i.e., $ϕ_2\sim\mathcal{O}(r^{-1})$. Given the constraint $|k_{AF}|\le10^{-44}$GeV \cite{CMBLV-N}, the three complex scalars $ϕ_a$ ($a=0,1,2$) still obey the peeling theorem: $ϕ_a\sim\mathcal{O}(r^{(a-3)}),~a=0,1,2$ for large, finite distances. |
| title | The asymptotic behavior of Lorentz-violating photon fields |
| topic | High Energy Physics - Phenomenology General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2410.04975 |