Deflection of charged signals in a dipole magnetic field in a Schwarzschild background using the Gauss-Bonnet theorem

Li, Zonghai; Wang, Wei; Jia, J.

doi:10.1103/physrevd.106.124025

Cited by 3 publications

(2 citation statements)

References 56 publications

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“…Comparing to the spinless case, the effect of nonzero j starts to manifest from the second order, i.e., the O (M/b) 2 order. This is similar to the effect of the spacetime spin [19] or the magnetic dipole on a charged signal [66]. Apparently, the sign of this term depends on the signs of s o and s j .…”

Section: Deflection Angle and Apparent Anglesmentioning

confidence: 66%

Effect of particle spin on trajectory deflection and gravitational lensing

Zhuoming

Fan

Jia

2022

J. Cosmol. Astropart. Phys.

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Spin of a test particle is a fundamental property that can affect its motion in a gravitational field. In this work we consider the effect of particle spin on its deflection angle and gravitational lensing in the equatorial plane of arbitrary stationary and axisymmetric spacetimes. To do this we developed a perturbative method that can be applied to spinning signals with arbitrary asymptotic velocity and takes into account the finite distance effect of the source and the observer. The deflection angle Δφ and total travel time Δt are expressed as (quasi-)power series whose coefficients are polynomials of the asymptotic expansion coefficients of the metric functions. It is found that when the spin and orbital angular momenta are parallel (or antiparallel), the deflection angle is decreased (or increased). Apparent angles θ of the images in gravitational lensing and their time delays are also solved. In Kerr spacetime, spin affects the apparent angle θK in a way similar to its effect on ΔφK . The time delay between signals with opposite spins is found to be proportional to the signal spin at leading order. These time delays might be used to constrain the spin to mass ratio of neutrinos.

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Section: Deflection Angle and Apparent Anglesmentioning

confidence: 66%

Effect of particle spin on trajectory deflection and gravitational lensing

Zhuoming

Fan

Jia

2022

J. Cosmol. Astropart. Phys.

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“…Specifically, in GWOIA method, the equatorial plane of the Riemannian part of a Rander-Finsler metric is selected as the two-dimensional Riemannian manifold, and the deflection angle is expressed in terms of the integral of the Gaussian curvature and the geodesic curvature. More related works for SAS spacetimes using GWOIA method can be found in [54][55][56][57][58][59][60][61][62][63][64][65][66][67][68].…”

Section: Jcap01(2024)013mentioning

confidence: 99%

Generalized Gibbons-Werner method for stationary spacetimes

Huang,

Cao,

2024

J. Cosmol. Astropart. Phys.

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The Gibbons-Werner (GW) method is a powerful approach in studying the gravitational deflection of particles moving in curved spacetimes. The application of the Gauss-Bonnet theorem (GBT) to integral regions constructed in a two-dimensional manifold enables the deflection angle to be expressed and calculated from the perspective of geometry. However, different techniques are required for different scenarios in the practical implementation which leads to different GW methods. For the GW method for stationary axially symmetric (SAS) spacetimes, we identify two problems: (a) the integral region is generally infinite, which is ill-defined for some asymptotically nonflat spacetimes whose metric possesses singular behavior, and (b) the intricate double and single integrals bring about complicated calculation, especially for highly accurate results and complex spacetimes. To address these issues, a generalized GW method is proposed in which the infinite region is replaced by a flexible region to avoid the singularity, and a simplified formula involving only a single integral of a simple integrand is derived by discovering a significant relationship between the integrals in conventional methods. Our method provides a comprehensive framework for describing the GW method for various scenarios. Additionally, the generalized GW method and simplified calculation formula are applied to three different kinds of spacetimes — Kerr spacetime, Kerr-like black hole in bumblebee gravity, and rotating solution in conformal Weyl gravity. The first two cases have been previously computed by other researchers, affirming the effectiveness and superiority of our approach. Remarkably, the third case is newly examined, yielding a innovative result for the first time.

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Deflection of charged signals in a dipole magnetic field in Kerr background

Li,

Jia

2024

Eur. Phys. J. C

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This paper investigates charged particle deflection in a Kerr spacetime background with a dipole magnetic field, focusing on the equatorial plane and employing the weak field approximation. We employ the Jacobi–Randers metric to unify the treatment of the gravitational and electromagnetic effects on charged particles. Furthermore, we utilize the Gauss–Bonnet theorem to calculate the deflection angle through curvature integrals. The difference between the prograde and retrograde deflection angles is linked to the non-reversibility of metrics and geodesics in Finsler geometry, revealing that this difference can be considered a Finslerian effect. We analyze the impact of both gravitomagnetic field and dipole magnetic field on particle motion and deflection using the Jacobi–Randers magnetic field. The model considered in this paper exhibits interesting features in the second-order approximation of (M/b), i.e., the ratio between the spacetime mass and impact parameters. When $$q\mu =2MaE$$ q μ = 2 M a E , where $$q,\,E$$ q , E are the charge and asymptotic energy of the charged particle and $$\mu ,\,a$$ μ , a are the dipole magnetic moment and spacetime spin, the Jacobi–Randers metric possesses reversible geodesics, leading to equal prograde and retrograde deflection angles. In this case, the gravitomagnetic field and dipole magnetic field cancel each other out, distinguishing it from scenarios involving only the gravitomagnetic field or the dipole magnetic field. We also explore the magnetic field’s impact on gravitational lensing of charged particles.

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Deflection of charged signals in a dipole magnetic field in a Schwarzschild background using the Gauss-Bonnet theorem

Cited by 3 publications

References 56 publications

Effect of particle spin on trajectory deflection and gravitational lensing

Effect of particle spin on trajectory deflection and gravitational lensing

Generalized Gibbons-Werner method for stationary spacetimes

Deflection of charged signals in a dipole magnetic field in Kerr background

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