Deflection of charged massive particles by a four-dimensional charged Einstein–Gauss–Bonnet black hole

Abstract

Based on the Jacobi metric method, this paper studies the deflection of a charged massive particle by a novel four-dimensional charged Einstein–Gauss–Bonnet black hole. We focus on the weak field approximation and consider the deflection angle with finite distance effects. To this end, we use a geometric and topological method, which is to apply the Gauss–Bonnet theorem to the Jacobi space to calculate the deflection angle. We find that the deflection angle contains a pure gravitational contribution δ g, a pure electrostatic δ c and a gravitational–electrostatic coupling term δ gc. We find that the deflection angle increases (decreases) if the Gauss–Bonnet coupling constant α is negative (positive). Furthermore, the effects of the BH charge, the particle charge-to-mass ratio and the particle velocity on the deflection angle are analyzed.

An alternative approach to study the phase transitions and stability Analysis of Kerr-Newman-Kasuya black hole

“…The study asserted that the weak deflection angle is more efficient in the detection of dark matter than shadow radius [16]. Z Li et al, discussed the perturbative approach generalized from the neutral signal case to investigate the deflection angle of charged signals in generic charged spacetime in the strong field limit [17]. Ali Övgün et al discussed the silhouette or shadow that a KNK spacetime creates.…”

Deflection in higher dimensional spacetime and asymptotically non-flat spacetimes

“…To theoretically investigate the deflection of these signals, recently two methods have been intensively used. One is to use the Gauss-Bonnet theorem method [21][22][23], which has been developed to handle both null and timelike signals [23][24][25][26], and to take into account the finite distance effect of the source and detector [27][28][29], as well as the electromagnetic force [26,29,30]. The other method is the perturbative method developed by some authors of this paper.…”

Deflection and gravitational lensing with finite distance effect in the strong deflection limit in stationary and axisymmetric spacetimes

“…Note that the study of the finite distance effect to the deflection angles and/or GL for null signals using the Gauss-Bonnet theorem method was initially carried out in ref. [46] in the weak deflection limit and then generalized to the SDL [47], the SAS [48] and asymptotically nonflat spacetimes [49], the timelike signal case [50] as well as with electrostatic interaction [51,52].…”

“…(2.36) and (2.37) not only contain the finite distance effect, but also the higher order terms, and work for timelike signals in addition to light rays. With the development of the Gauss-Bonnet theorembased methods [46][47][48][49][50][51][52], the computation of the deflection angles including in the SDL and with finite distance effect has also advanced tremendously. However our method provides a special and systematical way to tackle the time-related quantities in the SDL, on which there have been far fewer works so far.…”