Classical tests on a charged Weyl black hole: bending of light, Shapiro delay and Sagnac effect

Abstract

In this paper, we apply the classical test of general relativity on a charged Weyl black hole, whose exterior geometry is defined by altering the spherically symmetric solutions of Weyl conformal theory of gravity. The tests are basically founded on scrutinizing the angular geodesics of light rays propagating in the gravitating system caused by the black hole. In this investigation, we bring detailed discussions about the bending of light, together with two other relativistic effects, known as the Shapiro and the Sagnac effects. We show that the results are in good conformity with the general relativistic effects, besides giving long-distance corrections caused by the cosmological nature of the background geometry under study.

Ergosphere, Photon Region Structure, and the Shadow of a Rotating Charged Weyl Black Hole

“…The above values are those radii where the boundary of the photon region intersects with the cone θ = θ o . When a = 0, we have r pmax = r pmin = Q/ √ 2, which is the radius of the unstable photon orbits around a static CWBH, and it does not depend on λ [53]. This unique value corresponds to the constant value of ϑ p = π/2 for a = 0.…”

“…This solution is indeed the rotating counterpart of a particular static charged black hole, introduced in [52]. This charged Weyl black hole (CWBH) has been recently studied regarding the light propagation in vacuum and in plasmic medium [53,54] and the motion of neutral and charged particles [55,56]. As it is a rather interesting subject to understand how a black hole would appear in an observer's sky, it is therefore completely natural to discuss the optical properties of the rotating charged Weyl black hole (RCWBH) and its shadow.…”

“…Equations ( 26) and ( 57) imply that the inner photon ring is identified with the event horizon under the critical condition Q = Q ex , which corresponds to the extremal black hole, for which r p− = r + = r ex . Furthermore, the photon ring radii should also respect the condition 6 See the discussion in [53] on the photon trajectories around the static CWBH.…”

Роль Эллиптических Интегралов В Расчете Гравитационного Линзирования Заряженной Черной Дыры Вейля, Окруженной Плазмой

“…Therefore, exploiting Eqs. ( 27) to (30), the deflection angle for a light ray traveling from r ++ to R and goes again to r ++ , can be calculated as…”

“…This black hole has also been recently examined in Refs. [30,31,32], regarding the behavior of null and time-like geodesics passing its exterior geometry, where the elliptic functions played an important role in the determination of the mass-less and (charged) massive particle trajectories. The shadow structure of a rotating counterpart of this black hole has been also discussed in Ref.…”