Gravitational Lensing in Presence of Plasma: Strong Lens Systems, Black Hole Lensing and Shadow

Shadow and Weak Deflection Angle of a Black Hole in Nonlocal Gravity

Black hole shadow and gravitational lensing play important roles in testing gravitational theories in the strong field regime. As the first-order modifications from quantum gravity, the nonlocality can be manifested by black hole shadow and gravitational lensing. For example, the nonlocal parameter introduced by nonlocality will affect the shape and size of the black hole shadow, and also affect the deflection angle of light rays. In this paper, we mainly investigate the effects of the nonlocality on the black hole shadow and the gravitational lensing for two types of rotating black holes in nonlocal gravity. It is found that the size of the black hole shadow decreases with the nonlocal parameter since the nonlocality weakens the gravitational constant, and the shape of the shadow becomes more deformed with the increase in the nonlocal parameter. However, if the rotation parameter is small, the shape of the shadow is almost a circle even though the nonlocal parameter approaches its maximum. The energy emission rate in both models is also studied. The results show that there is a peak for each curve and the peak decreases and shifts to the low frequency with the increase in the nonlocal parameter. In addition, we also explore the shadow of both types of black holes surrounded by a nonmagnetized pressureless plasma which satisfies the separability condition. It is found that the plasma has a frequency-dependent dispersive effect on the size and shape of the black hole shadow. For the gravitational lensing, we find that the nonlocal parameter of model A makes a positive contribution to the deflection angle, which can be compared with the contribution of the rotation parameter, while the nonlocal parameter of model B makes a negative contribution which can be ignored. These results may be helpful for probing nonlocal gravity in future observations.

Weak Deflection Angle and Shadow by Tidal Charged Black Hole

In this article, we calculate the deflection angle of a tidal charged black hole (TCBH) in weak field limits. First, we obtain the Gaussian optical curvature and then apply the Gauss–Bonnet theorem on it. With the help of Gibbons–Werner method, we are able to calculate the light’s deflection angle by TCBH in weak field limits. After calculating the deflection angle of light, we check the graphical behavior of TCBH. Moreover, we further find the light’s deflection angle in the presence of the plasma medium and also check the graphical behavior in the presence of the plasma medium. Moreover, we investigate the shadow of TCBH. For calculating the shadow, we first find the null geodesics around the TCBH and then find its shadow radius. We also obtain TCBH’s shadow in the plasma medium. Hence, we discuss the shadow of the TCBH, using the M87* parameters announced by the event horizon telescope.

Visible Shapes of Black Holes M87* and SgrA*

We review the physical origins for possible visible images of the supermassive black hole M87* in the galaxy M87 and SgrA* in the Milky Way Galaxy. The classical dark black hole shadow of the maximal size is visible in the case of luminous background behind the black hole at the distance exceeding the so-called photon spheres. The notably smaller dark shadow (dark silhouette) of the black hole event horizon is visible if the black hole is highlighted by the inner parts of the luminous accreting matter inside the photon spheres. The first image of the supermassive black hole M87*, obtained by the Event Horizon Telescope collaboration, shows the lensed dark image of the southern hemisphere of the black hole event horizon globe, highlighted by accreting matter, while the classical black hole shadow is invisible at all. A size of the dark spot on the Event Horizon Telescope (EHT) image agrees with a corresponding size of the dark event horizon silhouette in a thin accretion disk model in the case of either the high or moderate value of the black hole spin, a≳0.75.