Non-linear effects on radiation propagation around a charged compact object

P. J. Pompeia,R. R. Cuzinatto,L. G. Medeiros,C. A. M. de Melo,K. C. de Vasconcelos

doi:10.1007/s10509-015-2505-2

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-Nordstr\"om 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.

Highlights

Generalizations of Maxwell electrodynamics have been proposed since it was established and they are motivated by several reasons such as experimental constraints on the eventual photon mass (Tu et al 2005; Cuzinatto et al 2011; Bonin et al 2010), classical aspects of vacuum polarization (Heisenberg and Euler 1936; Schwinger 1951), electrodynamics in the context of strings and superstrings (Seiberg and Witten 1999; Fradkin and Tseytlin 1985; Bergshoeff et al 1987; Metsaev et al 1987; Leigh 1989), etc
There is a group known as Nonlinear Electrodynamics (NLED) which is characterized by presenting nonlinear field equations
In Eq (44) the first term is the standard effect of classical electrostatics in the context of general relativity, the second term is the contribution from NLED effective metric, and the third one is the correction due to spacetime curvature coming from the nonlinear background electric field

Summary

Introduction

Generalizations of Maxwell electrodynamics have been proposed since it was established and they are motivated by several reasons such as experimental constraints on the eventual photon mass (Tu et al 2005; Cuzinatto et al 2011; Bonin et al 2010), classical aspects of vacuum polarization (Heisenberg and Euler 1936; Schwinger 1951), electrodynamics in the context of strings and superstrings (Seiberg and Witten 1999; Fradkin and Tseytlin 1985; Bergshoeff et al 1987; Metsaev et al 1987; Leigh 1989), etc. Examples of NLED are Born–Infeld theory (Born 1934, 1937; Born and Infeld 1934; Stehle and DeBaryshe 1966) and Euler–Heisenberg electrodynamics (Heisenberg and Euler 1936) The former was proposed to limit the maximum value of the electric field of a point charge (Delphenich 2003) and the last arises as an effective action of one-loop QED (Dunne 2005). Some preliminary results concerning photon propagation in non-linear interaction with a background electric field and in the presence of a BH were obtained in the context of Euler–Heisenberg and Born–Infeld electrodynamics (De Lorenci et al 2001; Bretón 2002). The authors intend to generalize these results for a generic NLED and show that, despite the fact that the background electric field does not generate effective horizons (horizons that would be sensed only by radiation), this field directly influences the geometric redshift and geodesic deviation. Fμν is the electromagnetic field tensor and F μν is its dual:

Effective metric

Influence of NLED on radiation propagation

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Geometric redshift

Geodesic deviation of radiation

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Conclusion