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.

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.

We study the effect of inhomogeneity, which is induced by the graviton mass in massive gravity, on the mutual information and the chaotic behavior of a 2+1-dimensional field theory from the gauge/gravity duality. When the system is near-homogeneous, the mutual information increases as the graviton mass grows. However, when the system is far from homogeneity, the mutual information decreases as the graviton mass increases. By adding the perturbations of energy into the system, we investigate the dynamical mutual information in the shock wave geometry. We find that the greater perturbations disrupt the mutual information more rapidly, which resembles the butterfly effect in chaos theory. Besides, the greater inhomogeneity reduces the dynamical mutual information more quickly just as in the static case.

We investigate the dynamical evolution of entanglement entropy in a holographic superconductor model by quenching the source term of the dual charged scalar operator. By access to the full background geometry, the holographic entanglement entropy is calculated for a strip geometry at the AdS boundary. It is found that the entanglement entropy exhibits a robust non-monotonic behaviour in time, independent of the strength of Gaussian quench and the size of the strip: it first displays a small dip, then grows linearly, and finally saturates. In particular, the linear growth velocity of the entanglement entropy has an upper bound for strip with large width; the equilibrium value of the non-local probe at late time shows a power law scaling behaviour with respect to the quench strength; moreover, the entanglement entropy can uncover the dynamical transition at certain critical quench strength which happens to coincide with the one obtained form the dynamical evolution of scalar order parameter.

We investigate the effect of massive graviton on the holographic thermalization process. Before doing this, we first find out the generalized Vaidya-AdS solutions in the de Rham-Gabadadze-Tolley (dRGT) massive gravity by directly solving the gravitational equations. Then, we study the thermodynamics of these Vaidya-AdS solutions by using the Minsner-Sharp energy and unified first law, which also shows that the massive gravity is in a thermodynamic equilibrium state. Moreover, we adopt the two-point correlation function at equal time to explore the thermalization process in the dual field theory, and to see how the graviton mass parameter affects this process from the viewpoint of AdS/CFT correspondence. Our results show that the graviton mass parameter will increase the holographic thermalization process.Comment: 15 pages, 2 figures, version published in PL

Traversing a continuous phase transition at a finite rate leads to the breakdown of adiabatic dynamics and the formation of topological defects, as predicted by the celebrated Kibble-Zurek mechanism (KZM). We investigate universal signatures beyond the KZM, by characterizing the distribution of vortices generated in a thermal quench leading to the formation of a holographic superconductor. The full counting statistics of vortices is described by a binomial distribution, in which the mean value is dictated by the KZM and higher-order cumulants share the universal power-law scaling with the quench time. Extreme events associated with large fluctuations no longer exhibit a power-law behavior with the quench time and are characterized by a universal form of the Weibull distribution for different quench rates.