Perturbative deflection angle for signal with finite distance and general velocities

Huang, Ke; Jia, J.

doi:10.1088/1475-7516/2020/08/016

Cited by 22 publications

(65 citation statements)

References 58 publications

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“…of Eq. ( 73) it is seen that the spacetime spin a would increases the deflection angle of retrograde particle ray, and decreases the deflection angle of prograde ray, as was known previously [76]. However, the effect of a when Q = 0 on the deflection of charged particles is different from that on neutral particles, due to the existence of the δ aqQ term.…”

Section: Discussion Of Resultssupporting

confidence: 57%

“…The most typical charged and rotating solution is the Kerr-Newman (KN) black hole [66,67], characterized by its mass, spin angular momentum and charge. In literature, the lensing of KN spacetime has been widely discussed such as equatorial light ray [68][69][70], any arbitrarily incident directions light ray [71], and equatorial neutral massive particle [72][73][74][75][76]. What is worth mentioning here is Jusufi's work on the deflection of charged particles in KN spacetime [64].…”

Section: Introductionmentioning

confidence: 99%

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Kerr-Newman-Jacobi geometry and the deflection of charged massive particles

Li,

Jia

2021

Preprint

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In this paper, we investigate the deflection of a charged particle moving in the equatorial plane of Kerr-Newman spacetime, focusing on weak field limit. To this end, we use the Jacobi geometry, which can be described in three equivalent forms, namely Randers-Finsler metric, Zermelo navigation problem, and (n + 1)-dimensional stationtary spacetime picture. Based on Randers data and Gauss-Bonnet theorem, we utilize osculating Riemannian manifold method and the generalized Jacobi metric method to study the deflection angle, respectively. In the (n + 1)-dimensional spacetime picture, the motion of charged particle follows the null geodesic, and thus we use the standard geodesic method to calculate the deflection angle. Three methods lead to the same second-order deflection angle, which is obtained for the first time. The result shows that the black hole spin a affects the deflection of charged particles both gravitationally and magnetically at the leading order (order O([M ] 2 /b 2 )). When qQ/E < 2M , a will decrease (or increase) the deflection of prograde (or retrograde) charged signal. If qQ/E > 2M , the opposite happens, and the ray is divergently deflected by the lens. We also showed that the effect of the magnetic charge of the dyonic Kerr-Newman black hole on the deflection angle is independent of the particle's charge.

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Section: Discussion Of Resultssupporting

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Kerr-Newman-Jacobi geometry and the deflection of charged massive particles

Li,

Jia

2021

Preprint

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“…Moreover, we adapt a perturbative method developed previously for the calculation of the deflection 0123456789(). : V,-vol angle and time delay in the weak field limit [33][34][35][36][37] to the SFL case, and use it to find a series form of the deflection angle for source and detector at finite distances. The leading two orders of this series will produce the deflection angle (1) when the asymptotic velocity is set to light speed and source/detector distances set to infinity.…”

Section: Introductionmentioning

confidence: 99%

Perturbative deflection angle, gravitational lensing in the strong field limit and the black hole shadow

Jia

Huang

2021

Eur. Phys. J. C

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A perturbative method to compute the deflection angle of both timelike and null rays in arbitrary static and spherically symmetric spacetimes in the strong field limit is proposed. The result takes a quasi-series form of $$(1-b_c/b)$$ ( 1 - b c / b ) where b is the impact parameter and $$b_c$$ b c is its critical value, with coefficients of the series explicitly given. This result also naturally takes into account the finite distance effect of both the source and detector, and allows to solve the apparent angles of the relativistic images in a more precise way. From this, the BH angular shadow size is expressed as a simple formula containing metric functions and particle/photon sphere radius. The magnification of the relativistic images were shown to diverge at different values of the source-detector angular coordinate difference, depending on the relation between the source and detector distance from the lens. To verify all these results, we then applied them to the Hayward BH spacetime, concentrating on the effects of its charge parameter l and the asymptotic velocity v of the signal. The BH shadow size were found to decrease slightly as l increases to its critical value, and increase as v decreases from light speed. For the deflection angle and the magnification of the images however, both the increase of l and decrease of v will increase their values.

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“…Previously, trajectory deflection and GL of neutral massive signals, including neutrinos and GWs in some gravitational theories beyond GR, have been studied by many researchers. The dependence of the deflection an-gle and GL observables on the general metric functions and signal properties have been studied in the weak field limit using both the perturbative method [21][22][23][24][25][26][27][28][29] and Gauss-Bonnet theorem method [30][31][32][33][34][35][36][37]. Recently, there is a resurgence of interest to study the deflection of charged massive particles (CMP) in charged spacetimes [32,38,39].…”

Section: Introductionmentioning

confidence: 99%

“…In this work we will study the deflection and the dual gravitational and electromagnetic lensing (GEL) of CMP in general charged static and spherical symmetric (SSS) spacetimes. We will investigate whether the perturbative method that was developed previously for neutral particles in general SSS or stationary axisymmetic spacetimes in the weak field limit [24][25][26][27][28] can be extended to the case with electromagnetic interaction. It turns out that the extension is possible with only a small modification of the derivation proceess (see Sec.…”

Section: Introductionmentioning

confidence: 99%

Deflection angle with electromagnetic interaction and gravitational-electromagnetic dual lensing

Xu,

Jiang,

Jia

2021

Preprint

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The trajectory deflection and gravitational-electromagnetic dual lensing (GEL) of charged signal in general charged static and spherically symmetric spacetimes are considered in this work. We showed that the perturbative approach previously developed for neutral particles can be extended to the electromagnetic interaction case. The deflection angle still takes a (quasi-)series form and the finite distance effect of both the source and observer can be taken into account. Comparing to pure gravitational case, the apparent angles of the images in the GEL, their magnifications and time delay all receive the electromagnetic corrections starting from the first non-trivial order. The sign and relative size of the leading corrections are determined by ∼ Q M q E where M, Q, q, E are the spacetime mass and charge, and signal particle charge and energy respectively. It is found that for qQ > 0 (or < 0), the electromagnetic interaction will decrease (or increase) the deflection angle, and in GEL the impact parameters, apparent angles, magnifications and total travel time for each image. The time delay is increased for small β and qQ > 0, and otherwise always increased regardless the sign of qQ. The results are then applied to the deflection and GEL of charged protons in cosmic rays in Reissner-Nordstrom, charged dilaton and charged Horndeski spacetimes.

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Perturbative deflection angle for signal with finite distance and general velocities

Cited by 22 publications

References 58 publications

Kerr-Newman-Jacobi geometry and the deflection of charged massive particles

Kerr-Newman-Jacobi geometry and the deflection of charged massive particles

Perturbative deflection angle, gravitational lensing in the strong field limit and the black hole shadow

Deflection angle with electromagnetic interaction and gravitational-electromagnetic dual lensing

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