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Shadow and Photon Sphere of Black Hole in Clouds of Strings and Quintessence

In this work, we study the shadow and photon sphere of the black bole in clouds of strings and quintessence with static and infalling spherical accretions. We obtain the geodesics of the photons near a black hole with different impact parameters $b$. The string clouds model and quintessence influence the specific intensity by affecting the geodesic and the average radial position of photons. And the range of string clouds parameter $a$ is constrained to ensure that the shadow can be observed. Moreover, we use a model of the photon emissivity $j(ν_e)$ to get the specific intensities. The light sources in the accretion follow a normal distribution with an attenuation factor $γ$. The shadow with static spherical accretion is plotted. The apparent shape of the shadow is a perfect circle, and the value of $γ$ affects the brightness of the photon sphere. We investigate the profile and specific intensity of the shadows with static and infalling spherical accretions respectively. The interior of the shadows with an infalling spherical accretion will be darker than that with the static spherical accretion, and the specific intensity with both static and infalling spherical accretion gradually converges.