[Paper Review] Nonlinear electrodynamics and the gravitational redshift of pulsars

Herman J. Mosquera Cuesta, J. M. Salim|arXiv (Cornell University)|Mar 2, 2004

Pulsars and Gravitational Waves Research3 citations

TL;DR

This paper investigates how Born-Infeld nonlinear electrodynamics (NLED) modifies the spacetime geometry around highly magnetized pulsars, particularly magnetars, by altering vacuum electromagnetic behavior. It demonstrates that this effect induces a significant gravitational redshift shift detectable in spectral lines, offering a potential observational signature of NLED beyond the Euler-Heisenberg approximation.

ABSTRACT

The idea that the nonlinear electromagnetic interaction, i. e., light propagation in vacuum, can be geometrized was developed by Novello et al. (2000) and Novello & Salim (2001). Since then a number of physical consequences for the dynamics of a variety of systems have been explored. In a recent paper Mosquera Cuesta & Salim (2003) presented the first astrophysical study where such nonlinear electrodynamics (NLEDs) effects were accounted for in the case of a highly magnetized neutron star or pulsar. In that paper the NLEDs was invoked {\\it a l\\`a} Euler-Heisenberg, which is an infinite series expansion of which only the first term was used for the analisys. The immediate consequence of that study was an overall modification of the space-time geometry around the pulsar, which is ``perceived'', in principle, only by light propagating out of the star. This translates into an significant change in the surface redshift, as inferred from absorption (emission) lines observed from a super magnetized pulsar. The result proves to be even more dramatic for the so-called magnetars, pulsars endowed with magnetic ($B$) fields higher then the Schafroth quantum electrodynamics critical $B$-field. Here we demonstrate that the same effect still appears if one calls for the NLEDs in the form of the one rigorously derived by Born & Infeld (1934) based on the special relativistic limit for the velocity of approaching of an elementary particle to a pointlike electron [From the mathematical point of view, the Born & Infeld (1934) NLEDs is described by an exact Lagrangean, whose dynamics has been successfully studied in a wide set of physical systems.].

Motivation & Objective

• To examine the impact of Born-Infeld nonlinear electrodynamics (NLED) on the spacetime geometry near highly magnetized neutron stars.
• To assess whether NLED effects—previously studied via the Euler-Heisenberg approximation—persist under the more rigorous Born-Infeld Lagrangian framework.
• To determine if such NLED-induced geometric modifications lead to observable changes in the gravitational redshift of spectral lines from pulsars.
• To evaluate the implications of NLED for magnetars, where magnetic fields exceed the Schwinger critical field.

Proposed method

• Adopting the exact Born-Infeld Lagrangian as the foundation for nonlinear electrodynamics, which avoids perturbative expansions.
• Applying the Born-Infeld NLED framework to model vacuum polarization effects in strong magnetic fields typical of pulsars.
• Deriving corrections to the spacetime metric around a pulsar due to the modified electromagnetic stress-energy tensor from NLED.
• Analyzing the resulting gravitational redshift of spectral lines using the modified metric, comparing it to standard general relativity predictions.
• Focusing on the regime of magnetars, where magnetic fields approach or exceed the Schwinger critical field (~4.4×10^13 G).

Experimental results

Research questions

• RQ1 Does the Born-Infeld formulation of nonlinear electrodynamics produce a measurable modification to the gravitational redshift in pulsars?
• RQ2 How does the inclusion of the exact Born-Infeld Lagrangian affect the spacetime geometry compared to the Euler-Heisenberg approximation?
• RQ3 Can NLED effects in magnetars lead to a detectable shift in the observed redshift of emission or absorption lines?
• RQ4 Is the NLED-induced geometric modification purely observable via light propagation, as predicted by the theory?

Key findings

• The Born-Infeld NLED framework leads to a significant modification of the spacetime geometry around highly magnetized pulsars.
• This geometric change results in a measurable shift in the gravitational redshift as inferred from spectral lines, even when the magnetic field exceeds the Schwinger critical field.
• The effect persists even when using the exact Born-Infeld Lagrangian, confirming that the result is not an artifact of the perturbative Euler-Heisenberg approximation.
• The modification is perceived exclusively by light propagating through the vacuum, consistent with the idea that NLED alters vacuum optical properties.
• The study confirms that NLED effects are more pronounced in magnetars due to their extreme magnetic fields, making them prime candidates for testing nonlinear electrodynamics.