Abstract
The propagation of non-linear electromagnetic waves is carefully analyzed on a curved spacetime created by static spherically symmetric mass and charge distribution. We compute how non-linear electrodynamics affects the geodesic deviation and the redshift of photons propagating near this massive charged object. In the first order approximation, the effects of electromagnetic self-interaction can be distinguished from the usual Reissner–Nordström terms. In the particular case of Euler–Heisenberg effective Lagrangian, we find that these self-interaction effects might be important near extremal compact charged objects.
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Notes
In flat spacetime, \(F = ( \vec{E}^{2}-\vec{B}^{2} ) / 2 \) and \(G=\vec{E}\cdot\vec{B}\). The vectors \(\vec{E}\) and \(\vec{B}\) are the electric and magnetic fields respectively. F and G are the only Lorentz and gauge invariant functions of \(F_{\mu\nu}\) (Delphenich 2006).
Energies much less than that of the electron rest energy.
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KCV acknowledges CAPES-Brazil for financial support. LGM is grateful to FAPERN-Brazil for financial support.
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Cuzinatto, R.R., de Melo, C.A.M., de Vasconcelos, K.C. et al. Non-linear effects on radiation propagation around a charged compact object. Astrophys Space Sci 359, 59 (2015). https://doi.org/10.1007/s10509-015-2505-2
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DOI: https://doi.org/10.1007/s10509-015-2505-2