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We study the holographic entanglement entropy under small deformations of AdS, including time-dependence. It is found through perturbative analysis that the divergent terms are not affected and the change appears only in the finite terms. We also consider the entanglement thermodynamic first law, and calculate the entanglement temperature and confirm that it is inversely proportional to the size of the entangling region.
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We study holographic entanglement entropy in Gauss-Bonnet gravity following a global quench. It is known that in dynamical scenarios the entanglement entropy probe penetrates the apparent horizon. The goal of this work is to study how far behind the horizon can the entanglement probe reach in a Gauss-Bonnet theory. We find that the behavior is quite different depending on the sign of the Gauss-Bonnet coupling $lambda_{GB}$. We show that for $lambda_{GB} > 0$ the holographic entanglement entropy probe explores less of the spacetime behind the horizon than in Einstein gravity. On the other hand, for $lambda_{GB} < 0$ the results are strikingly different; for early times a new family of solutions appears. These new solutions reach arbitrarily close to the singularity. We calculate the entanglement entropy for the two family of solutions with negative coupling and find that the ones that reach the singularity are the ones of less entropy. Thus, for $lambda_{GB} < 0$ the holographic entanglement entropy probes further behind the horizon than in Einstein gravity. In fact, for early times it can explore all the way to the singularity.
The BPS D3 brane has a non-supersymmetric cousin, called the non-susy D3 brane, which is also a solution of type IIB string theory. The corresponding counterpart of black D3 brane is the `black non-susy D3 brane and like the BPS D3 brane, it also has a decoupling limit, where the decoupled geometry (in the case we are interested, this is asymptotically AdS$_5$ $times$ S$^5$) is the holographic dual of a non-conformal, non-supersymmetric QFT in $(3+1)$-dimensions. In this QFT we compute the entanglement entropy (EE), the complexity and the Fisher information metric holographically using the above mentioned geometry for spherical subsystems. The fidelity and the Fisher information metric have been calculated from the regularized extremal volume of the codimension one time slice of the bulk geometry using two different proposals in the literature. Although for AdS black hole both the proposals give identical results, the results differ for the non-supersymmetric background.
We review the results of refs. [1,2], in which the entanglement entropy in spaces with horizons, such as Rindler or de Sitter space, is computed using holography. This is achieved through an appropriate slicing of anti-de Sitter space and the implementation of a UV cutoff. When the entangling surface coincides with the horizon of the boundary metric, the entanglement entropy can be identified with the standard gravitational entropy of the space. For this to hold, the effective Newtons constant must be defined appropriately by absorbing the UV cutoff. Conversely, the UV cutoff can be expressed in terms of the effective Planck mass and the number of degrees of freedom of the dual theory. For de Sitter space, the entropy is equal to the Wald entropy for an effective action that includes the higher-curvature terms associated with the conformal anomaly. The entanglement entropy takes the expected form of the de Sitter entropy, including logarithmic corrections.
We investigate holographic cosmologies appearing in the braneworld model with a uniformly distributed $p$-brane gas. When $p$-branes extend to the radial direction, an observer living in the brane detects $(p-1)$-dimensional extended objects. On this background, we show that the braneworld model reproduces the expanding universes of the standard cosmology. In an expanding universe with a matter, we investigate the entanglement entropy between the visible and invisible universes across the cosmological (or particle) horizon. We show that, though the visible and invisible universes are causally disconnected, the nonlocal quantum correlation gives rise to a nontrivial time-dependent entanglement entropy relying on the matter.
The thermalization process of the holographic entanglement entropy (HEE) of an annular domain is investigated over the Vaidya-AdS geometry. We numerically determine the Hubeny-Rangamani-Takayanagi (HRT) surface which may be a hemi-torus or two disks, depending on the ratio of the inner radius to the outer radius of the annulus. More importantly, for some fixed ratio of two radii, it undergoes a phase transition or double phase transitions from a hemi-torus configuration to a two-disk configuration, or vice versa, during the thermalization. The occurrence of various phase transitions is determined by the ratio of two radii of the annulus. The rate of entanglement growth is also investigated during the thermal quench. The local maximal rate of entanglement growth occurs in the region with double phase transitions. Finally, if the quench process is fairly slow which may be controlled by the thickness of null shell, the region with double phase transitions vanishes.
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