We investigate the effects of quintessence dark energy on the shadows of black hole, surrounded by various profiles of accretions. For the thin-disk accretion, the images of the black hole comprises the dark region and bright region, including direct emission, lensing rings and photon rings. Although their details depend on the form of the emission, generically, direct emission plays a major role for the observed brightness of the black hole, while the lensing ring makes a small contribution and the photon ring makes a negligible contribution. The existence of a cosmological horizon also plays an important role in the shadows, since the observer in the domain of outer communications is near the cosmological horizon. For spherically symmetric accretion, static and infalling matters are considered. We find that the positions of photon spheres are the same for both static and infalling accretions. However, the observed specific intensity of the image for infalling accretion is darker than for static accretion, due to the Doppler effect of the infalling motion.

The phase structure of holographic entanglement entropy is studied in massive gravity for the quantum systems with finite and infinite volumes, which in the bulk is dual to calculate the minimal surface area for a black hole and black brane respectively. In the entanglement entropy$-$temperature plane, we find for both the black hole and black brane there is a Van der Waals-like phase transition as the case in thermal entropy$-$temperature plane. That is, there is a first order phase transition for the small charge and a second order phase transition at the critical charge. For the first order phase transition, the equal area law is checked and for the second order phase transition, the critical exponent of the heat capacity is obtained. All the results show that the phase structure of holographic entanglement entropy is the same as that of thermal entropy regardless of the volume of the spacetime on the boundary.Comment: 15 pages, many figures, some statments are adde

We investigate the shadows and photon spheres of the four-dimensional Gauss–Bonnet black hole with the static and infalling spherical accretions. We show that, for both cases, there always exist shadows and photon spheres. The radii of the shadows and photon spheres are independent of the profiles of accretion for a fixed Gauss–Bonnet constant, implying that the shadow is a signature of the spacetime geometry and it is hardly influenced by accretion. Because of the Doppler effect, the shadows of the infalling accretion are found to be darker than in the static case. We also investigate the effect of the Gauss–Bonnet constant on the shadow and photon spheres, and we find that the larger the Gauss–Bonnet constant is, the smaller the radii of the shadow and photon spheres will be. In particular, the observed specific intensity increases as the Gauss–Bonnet constant grows.