Letter: Nonlinear Gravitational-Electromagnetic Bending of the Rays of Weak Electromagnetic Waves in the Fields of Pulsars and Magnetars

Denisova, I. P.; Krivchenkov, I. V.; Vshivtseva, P. A.; Zubrilo, A. A.

doi:10.1023/b:gerg.0000017041.47194.4b

Cited by 7 publications

(6 citation statements)

References 11 publications

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“…Three nonlinear vacuum electrodynamics models are considered in the contemporary literature: the Born-Infeld electrodynamics [5], the nonlinear Heisenberg-Euler electrodynamics [6], and the parameterized post-Maxwellian electrodynamics [7].…”

Section: Finding the Metric Tensor Of The Effective Riemannian Space mentioning

confidence: 99%

Developing the eikonal method in nonlinear electrodynamics based on the geometrization principle

Krivchenkov

2007

Theor Math Phys

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We derive the eikonal equation for an electromagnetic wave propagating in an external electromagnetic field according to the laws of nonlinear electrodynamics. Based on Logunov's geometrization principle, we determine the metric tensors of the effective Riemannian spaces for the Born-Infeld electrodynamics, nonlinear Heisenberg-Euler electrodynamics, and a parameterized post-Maxwellian electrodynamics. We analyze the main properties of these nonlinear electrodynamics.

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Section: Finding the Metric Tensor Of The Effective Riemannian Space mentioning

confidence: 99%

Developing the eikonal method in nonlinear electrodynamics based on the geometrization principle

Krivchenkov

2007

Theor Math Phys

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“…В современной научной литературе рассматриваются три модели нелинейной электродинамики вакуума: электродинамика Борна-Инфельда [5], нелинейная электродинамика Гейзенберга-Эйлера [6] и параметризованная постмаксвелловская электродинамика [7]. В нелинейной электродинамике Борна-Инфельда функция L имеет вид…”

Section: определение метрического тензора эффективного риманова простunclassified

Развитие Метода Эйконала В Нелинейной Электродинамике На Основе Принципа Геометризации

Krivchenkov¹

2007

ТМФ

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Выведено уравнение эйконала для электромагнитной волны, распространяющейся во внешнем электромагнитном поле по законам нелинейной электродинамики. На основе принципа геометризации Логунова определены метрические тензоры эффективных римановых пространств для электродинамики Борна-Инфельда, нелинейной электродинамики Гейзенберга-Эйлера и параметризованной постмаксвелловской электродинамики. Проанализированы основные свойства этих нелинейных электродинамик.

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“…Therefore, propagation of a weak electromagnetic wave in an external electromagnetic field is accompanied by several nonlinear electrodynamic effects similar to the nonlinear optical effect. In particular, the effects that occur during propagation of electromagnetic waves in a magnetic dipole field include a photon splitting into two photons [4], generation of the second harmonic [5], nonlinear electrodynamic bending of electromagnetic wave rays [6], [7], and the vacuum-birefringence-induced nonlinear electrodynamic retardation of the electromagnetic signal [8], [9] carried by one normal wave compared with the electromagnetic signal carried by the other normal wave.…”

mentioning

confidence: 99%

“…(6) and all the subsequent relations obtained from them hold only in the spatial domain where m 2 /r 6 < B 2 q and the expansion of Lagrangian (2) is applicable. In what follows, we therefore investigate only those weak electromagnetic wave beams that are fully confined within this spatial domain.…”

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confidence: 99%

Nonlinear electrodynamic lensing of electromagnetic waves in a magnetic dipole field

2007

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We consider propagation of electromagnetic waves in magnetic dipole and gravitational fields proceeding in accordance with the nonlinear vacuum electrodynamics laws. We derive formulas describing the effect of nonlinear electrodynamic lensing of electromagnetic waves in the magnetic dipole field. We show that rotation of the magnetic dipole moment about an axis noncoincident with this moment leads to a nonlinear electrodynamic modulation of the electromagnetic radiation intensity by frequencies that are multiples of the dipole rotation frequency.In modern theoretical models, it is known [1]-[3] that the vacuum electrodynamics is a nonlinear theory. Therefore, propagation of a weak electromagnetic wave in an external electromagnetic field is accompanied by several nonlinear electrodynamic effects similar to the nonlinear optical effect. In particular, the effects that occur during propagation of electromagnetic waves in a magnetic dipole field include a photon splitting into two photons [4], generation of the second harmonic [5], nonlinear electrodynamic bending of electromagnetic wave rays [6], [7], and the vacuum-birefringence-induced nonlinear electrodynamic retardation of the electromagnetic signal [8], [9] carried by one normal wave compared with the electromagnetic signal carried by the other normal wave.Any ray bending is accompanied by lensing, which results in a redistribution of the electromagnetic wave energy flux, leading to intensity increases in certain spatial domains and decreases in others. The effect of nonlinear electrodynamic lensing of electromagnetic waves, similar to the gravitational lensing effect, is therefore observed in a dipole magnetic field [10], [11]. We study its principal features.We consider a single neutron star with a strong magnetic field (a pulsar or a magnetar) with the radius R s , mass M , and magnetic dipole moment m. Let the electromagnetic radiation from a remote source pass through the magnetic and gravitational fields of this star. We place the coordinate origin at the neutron star center and direct the Cartesian coordinate axes such that the wave vector of the incident plane electromagnetic wave is directed along the z axis.Because the neutron stars have a magnetosphere filled with matter, we consider the nonlinear electrodynamic lensing effect for electromagnetic radiation in the X-ray and gamma spectral range. For these frequencies, the refraction index of matter [12] is close to unity, and the magnetosphere is transparent to a certain degree. The sources of such radiation for the pulsar or magnetar under consideration can be remote astrophysical objects such as the nuclei of active galaxies (a blazar, quasar, or Seyfert galaxy) or galactic clusters. In the neighborhood of the pulsar or magnetar, the incident electromagnetic wave can then be considered plane.

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Letter: Nonlinear Gravitational-Electromagnetic Bending of the Rays of Weak Electromagnetic Waves in the Fields of Pulsars and Magnetars

Cited by 7 publications

References 11 publications

Developing the eikonal method in nonlinear electrodynamics based on the geometrization principle

Developing the eikonal method in nonlinear electrodynamics based on the geometrization principle

Развитие Метода Эйконала В Нелинейной Электродинамике На Основе Принципа Геометризации

Nonlinear electrodynamic lensing of electromagnetic waves in a magnetic dipole field

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