Strong gravitational lensing by a rotating non-Kerr compact object

We study the strong gravitational lensing in the background of a rotating non-Kerr compact object with a deformed parameter $ϵ$ and an unbound rotation parameter $a$. We find that the marginally circular stable orbit radius and the deflection angle depend sharply on the parameters $ϵ$ and $a$. For the case in which the black hole is more prolate than a Kerr black hole, the marginally circular photon orbit exists only in the regime $ϵ\le {ϵ}_{\max }$ for a prograde photon. The upper limit ${ϵ}_{\max }$ is a function of the rotation parameter $a$. As $ϵ>{ϵ}_{\max }$, the deflection angle of the light ray very close to the naked singularity is a positive finite value, which is different from that in the rotating naked singularity described by Janis-Newman-Winicour metric. For the oblate black hole and the retrograde photon, there does not exist such a threshold value. Modeling the supermassive central object of the Galaxy as a rotating non-Kerr compact object, we estimated the numerical values of the coefficients and observables for gravitational lensing in the strong field limit.

Figure 1

Variety of the marginally circular orbit radius of the photon with the deformed parameter $ϵ$ for different $a$. Here, we set $2M=1$.

Figure 2

Deflection angle $\alpha (x_0)$ as a function of the closest distance of approach $x_0$ for angular momentum $a<0$. Here, we set $2M=1$.

Figure 3

Deflection angle $\alpha (x_0)$ as a function of the closest distance of approach $x_0$ for angular momentum $a=0$. Here, we set $2M=1$.

Figure 4

Deflection angle $\alpha (x_0)$ as a function of the closest distance of approach $x_0$ for angular momentum $a>0$. Here, we set $2M=1$.

Figure 5

Variety of the deflection angle ${\alpha }_s$ with the deformed parameter $ϵ$ and the angular momentum $a$ as the light ray is very close to the singularity. Here, we set $2M=1$.

Figure 6

Change of the strong deflection limit coefficients with the deformed parameter $ϵ$ for different $a$ in the rotating non-Kerr spacetime. Here, we set $2M=1$.

Figure 7

Deflection angles evaluated at $u=u_{\mathrm{ps}}+0.003$ as a function of the deformed parameter $ϵ$ for different $a$. Here, we set $2M=1$.

Figure 8

Variety of the innermost relativistic image ${\theta }_{\infty }$ with the deformed parameter $ϵ$ for different $a$. Here, we set $2M=1$.

Figure 9

Variety of the angular separation $s$ with the deformed parameter $ϵ$ for different $a$. Here, we set $2M=1$.

Figure 10

Variety of the relative magnitudes $r_m$ with the deformed parameter $ϵ$ for different $a$. Here, we set $2M=1$.