Analytical derivation of second-order deflection in the equatorial plane of a radially moving Kerr–Newman black hole

Abstract

In this work, we base on the second-order post-Minkowskian equations of motion, and apply an iterative technique to analytically derive the gravitational deflection of the relativistic particles in the equatorial plane of Kerr-Newman black hole with a radial (or longitudinal) and constant velocity. We find that the kinematically correctional effects on the second-order contributions to the deflection can be expressed into a very compact form, which are valid for both the massive particle and photon. Our result reduces to the previous formulation for the first-order deflection caused by a moving Schwarzschild black hole when the second-order contributions are dropped.

Gravitational Deflection of Massive Particles by a Schwarzschild Black Hole in Radiation Gauge*

“…Recently, He and Lin [10] considered the gravitational deflection of relativistic massive particles and light caused by a moving Kerr-Newman source numerically, and found that the second-order Schwarzschild contribution was in agreement with the former. This consistency was further confirmed by the analytical calculation via an iterative technique [11]. There were also other investigations devoted to the deflection of massive particles in static and spherically symmetric spacetimes [12][13][14], with their results matching with the Accioly and Ragusa's proposal.…”

“…Ref. [11]. Since different gauge leads to different coordinates for a given geometry, we actually verify further that the gravitational deflection angle of a test particle is independent on concrete coordinates, including the radiation-gauge coordinates [15,16].…”

“…In this article, we calculate the gravitational deflection of relativistic test particles including light up to the 4PM order in this gravity, based on the iterative technique proposed in Ref. [11]. Our discussions are constrained in the weak-field, small-angle, and thin-lens approximation.…”

Weak and strong deflection gravitational lensing by a renormalization group improved Schwarzschild black hole

“…Therefore, we only provide some hints of its gravitational lensing signals. More sophisticated investigations with inclusion of its spin in the weak [97][98][99][100][101][102][103][104][105][106][107][108][109][110][111][112][113] and strong [114][115][116][117][118] deflection lensing as well as general relativistic magnetohydrodynamics of plasma are indeed needed.…”

Null gravitational redshift by a Reissner–Nordström black hole in the strong field limit

“…with the affine parameter ξ B of the observer being given to be X B in the asymptotically flat spacetime [49,51]. It is worth to point out that there might be several numerical values of ξ A to correspond to a given X A in the strong field limit, and we take the one whose value is closest to X A in the following calculations for physical reasons.…”