Strong gravitational lensing for photons coupled to Weyl tensor in a regular phantom black hole

Abstract

We study strong gravitational lensing for photons coupled to Weyl tensor in a regular phantom black hole spacetime. It is generally accepted that photons with different polarizations have different trajectories which yields a phenomenon of birefringence. As a result, there are two sets of relativistic images on each side of the object, this is quite different from the uncoupled case in which there is only one set of images. Nevertheless, we focus our attention on the relativistic images on one side of the object and investigate the difference between them by discussing how the coupling constant and phantom hair affect the difference of photon sphere radius, minimum impact parameter and deflection angle. After that, we find that the closer the light gets to the black hole, the larger the deflection angle will be. Then, we investigate the difference in angular image position and relative magnitudes of the first relativistic image between the two types of polarized photons, and find that the two images for different polarizations will separate further and be distinguished more easily in the cases that the phantom hair decreases or the absolute value of the coupling constant increases. Furthermore, the image is brighter when it seats closer to the optical axis.

Time delay of photons coupled to Weyl tensor in a regular phantom black hole

“…In the present work, in order to obtain a more comprehensive picture of the photons coupled to the Weyl tensor in the regular phantom black hole, we investigate its time delay in both weak and strong deflection gravitational lensing, which is absent in the previous work [88]. These time-domain signals are important for determining the properties of black holes [89][90][91][92][93][94] and probing new physics [95][96][97][98][99][100][101][102].…”

“…The weak and strong deflection gravitational lensing of the phantom black holes were investigated under the standard Einstein-Maxwell theory [85][86][87]. Considering the photons coupled to the Weyl tensor in the regular phantom black hole, its strong deflection gravitational lensing was studied and the positions and brightness difference of the resulting relativistic images were analyzed [88].…”

“…In Sect. 2, we briefly review the effective metric of the photons coupled to the Weyl tensor in the regular phantom black hole and carefully find its parameter space which was missing in the previous work [88]. Meanwhile, the set-up for gravitational lensing is also given.…”

“…Therefore, the effective metric of the photons coupled to the Weyl tensor in the regular phantom black hole can be obtained as [88] ds 2 = −A(r )dt 2…”

“…15, is slightly different from the one of the work [73] about the photons coupled to the Weyl tensor in the Schwarzschild black hole. Before we proceed, it is necessary to determine the domain of {b,α • } which has not been intensively investigated in the previous work [88]. In order to ensure the validity of the effective metric (13), its coefficients have to keep their properties of either time-like or space-like unchanged during the propagation of the photon, i.e.,…”