Weak deflection angle and shadow cast by the charged-Kiselev black hole with cloud of strings in plasma*

Abstract

In this work, the gravitational deflection angle of photon in the weak field limit (or the weak deflection angle) and shadow cast by the electrically charged and spherically symmetric static Kiselev black hole (BH) in the string cloud background are investigated. The influence of the BH charge $Q$, the quintessential parameter $\gamma$ and the string cloud parameter $a$ is studied on the weak deflection angle using the Gauss-Bonnet theorem, on the radius of photon spheres and on the size of the BH shadow in the spacetime geometry of the charged-Kiselev BH in string clouds. Moreover, we study the effects of plasma (uniform and non-uniform) on the weak deflection angle and on the shadow cast by the charged-Kiselev BH surrounded by the clouds of strings. In the presence of uniform/nonuniform plasma medium, increase in the cloud of string parameter $a$, increases the deflection angle $\alpha$. On the other hand decrease in the BH charge $Q$, decreases the deflection angle. Further we observe that an increase of the BH charge $Q$ causes a decrease in the size of the shadow of the BH. We notice that with increase in the values of the parameters $\gamma$ and $a$, the size of the BH shadow also increases and therefore the intensity of the gravitational field around the charged-Kiselev BH in string clouds increases. Thus the gravitational field of the charged-Kiselev BH in string cloud background would be stronger than the field produced by the pure Reissner-Nordstrom BH. Moreover, we use the data released by the Event Horizon Telescope (EHT) collaboration, for the supermassive BHs M87* and Sgr A*, to obtain constraints on the values of the parameters $\gamma$ and $a$.

Probing geometric proca in metric-palatini gravity with black hole shadow and photon motion

“…α sh is the angular radius of the BH shadow, r obs is observer distance and r ph is already introduced in the previous subsection. The Observer distance is very large but finite, and it has the value r obs = D = 8.3 kpc for the Sgr A* [106] or r obs = D = 16.8 Mpc for the M87* [62]. Now we combine Eqs.…”

“…The first black hole shadow has been observed by Event Horizon Telescope observing at a wavelength of 1.3 mm, in 2019, the image of M87* (which has 6.5 ± 0.7 billion solar masses, located at 16.8 kpc) with the angular size 42 ± 3 µas with the observational resolution 20 µas [62]. Three years later, in 2022, the image of the central part of the Milky Way galaxy, known as Sgr A* (with 4 +1.1 −0.6 million solar masses, located at about 8 kpc), has also been observed with shadow size 48.7 ± 7 µas together with the radiation ring with the size 51.8 ± 2.3 µas [106]. The appearance of the radiation ring may be due to the presence of a plasma medium around Srg A*.…”

“…Even before the first ever observation of the BH shadow in 2019 by the Event Horizon Telescope collaboration [62,63] various authors have studied the shadow of the black hole/compact objects within general relativity and modified/alternative theories of gravity (see, e.g. [64][65][66][67][68][68][69][70][71][72][72][73][74][75][76][77][77][78][79][80][81][82][83][84][84][85][86][87][88][89][90][91][92][93][94][95][96][97][98]) and also the authors studied the effect of plasma on the BH shadow in [99][100][101][102][103][104][105]. Observation data on the shadow of supermassive BHs at the center of M87…”

“…[64][65][66][67][68][68][69][70][71][72][72][73][74][75][76][77][77][78][79][80][81][82][83][84][84][85][86][87][88][89][90][91][92][93][94][95][96][97][98]) and also the authors studied the effect of plasma on the BH shadow in [99][100][101][102][103][104][105]. Observation data on the shadow of supermassive BHs at the center of M87 [62] and Sgr A* [106] are used to get estimations and/or constraints of BH parameters within different gravity models [107].…”

Testing symmergent gravity through the shadow image and weak field photon deflection by a rotating black hole using the M87$$^*$$ and Sgr. $$\hbox {A}^*$$ results

“…It would take more years, or even more sophisticated equipment, to probe other theories of gravity using the black hole. Ever since many authors have considered exploring the behavior of the classical shadow silhouette for black holes [15,18] described by either a toy model metric or through an alternative theory of gravity [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”