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The concept of the generalized entanglement wedge was recently proposed by Bousso and Penington, which states that any bulk gravitational region $a$ possesses an associated generalized entanglement wedge $E(a)\supset a$ on a static Cauchy surface $M$ in general gravitational spacetimes, where $E(a)$ may contain an entanglement island $I(a)$. It suggests that the fine-grained entropy for bulk region $a$ is given by the generalized entropy $S_{\text{gen}}(E(a))$. Motivated by this proposal, we extend the quantum bit thread description to general gravitational spacetimes, no longer limited to the AdS spacetime. By utilizing the convex optimization techniques, a dual flow description for the generalized entropy $S_{\text{gen}}(E(a))$ of a bulk gravitational region $a$ is established on the static Cauchy surface $M$, such that $S_{\text{gen}}(E(a))$ is equal to the maximum flux of any flow that starts from the boundary $\partial M$ and ends at bulk region $a$, or equivalently, the maximum number of bit threads that connect the boundary $\partial M$ to the bulk region $a$. In addition, the nesting property of flows is also proved. Thus the basic properties of the entropy for bulk regions, i.e. the monotonicity, subadditivity, Araki-Lieb inequality and strong subadditivity, can be verified from flow perspectives by using properties of flows, such as the nesting property. Moreover, in max thread configurations, we find that there exists some lower bounds on the bulk entanglement entropy of matter fields in the region $E(a)\setminus a$, particularly on an entanglement island region $I(a) \subset (E(a)\setminus a)$, as required by the existence of a nontrivial generalized entanglement wedge. Our quantum bit thread formulation may provide a way to investigate more fine-grained entanglement structures in general spacetimes., Comment: 32 pages, 4 figures; improvements to presentation; Figure 2 and Footnote 10 are added; published version in JHEP

We study the information paradox of Reissner-Nordstr${\ddot{o}}$m anti-de Sitter (RN-AdS$_{d+1}$) black holes in the large dimension limit by using the island formula. The entanglement entropy of Hawking radiation is calculated both for the non-extremal and the extremal cases, in which the boundary of the radiation region is close to the outer horizon. For the non-extremal case, the entanglement entropy of Hawking radiation obeys the Page curve, i.e. the entanglement entropy of Hawking radiation increases with time and reaches saturation about twice Bekenstein-Hawking entropy at the Page time. For the extremal case, the entanglement entropy of Hawking radiation becomes ill-defined in the absence of the island due to the appearance of the singularity at the origin of the radial coordinate, while when the island exists, the entanglement entropy is found to be equal to the Bekenstein-Hawking entropy. In addition, for the case where the boundary of the radiation region is close to the horizon, there are some obvious constraints required by the existence of island solution for both non-extremal and extremal cases, which can be utilized to put constraints on the size of the black hole. These results reveal new features of the semi-classical large $d$ black holes from the island perspective., Comment: 25 pages, 7 figures

We reconsider $D\geq4$ dimensional asymptotically flat eternal Schwarzschild black hole, and focus on the situation where the inner boundary of the radiation region is chosen to be near the horizon (i.e. $\beta \ll1$). The tension between the near-horizon condition and the short-distance approximation emerges in large dimensions in $[JHEP 06 (2020) 085]$. We remove this tension by introducing a more proper near horizon condition, thus the resulting island solution is well-behaved in any $D\geq4$ dimensional spacetime. Interestingly, a novel constraint is obtained in this situation as required by the existence of the island solution, which directly leads to the constraints on the size of the Schwarzschild black hole, the position of the inner boundary for the radiation region, or the value of $c\cdot\tilde{G}_{N}$ in any $D\geq4$ dimension. When considering the large $D$ limit, the constraint on the size of the Schwarzschild black hole obtained in this situation is in agreement with the result given in $[Phys.Rev.D 102 (2020) 2, 026016]$. We interpret these as the unitary constraints implied by the presence of island in semiclassical gravity., Comment: 21 pages, 4 figures; improvements to the expression; Footnote 2 added to show a new analytical island solution for $n\rightarrow\infty$ while $\alpha\sim \beta/n$; accepted for publication in PRD

The celebrated holographic entanglement entropy triggered investigations on the connections between quantum information theory and quantum gravity. An important achievement is that we have gained more insights into the quantum states. It allows us to diagnose whether a given quantum state is a holographic state, a state whose bulk dual admits semiclassical geometrical description. The effective tool of this kind of diagnosis is holographic entropy cone (HEC), an entropy space bounded by holographic entropy inequalities allowed by the theory. To fix the HEC and to prove a given holographic entropy inequality, a proof-by-contraction technique has been developed. This method heavily depends on a contraction map $f$, which is very difficult to construct especially for more-region ($n\geq 4$) cases. In this work, we develop a general and effective rule to rule out most of the cases such that $f$ can be obtained in a relatively simple way. In addition, we extend the whole framework to relative homologous entropy, a generalization of holographic entanglement entropy that is suitable for characterizing the entanglement of mixed states., Comment: 1+27 pages; Version matches published one in JHEP

Great breakthrough in solving black hole information paradox took place when semiclassical island rule for entanglement entropy of Hawking radiation was proposed in recent years. Up to now, most papers which discussed island rule of asymptotic flat black hole with $D \ge 4$ focus on eternal black hole. In this paper, we take one more step further by discussing island of "in" vacuum state which describes one-sided asymptotically flat black hole formed by gravitational collapse in $D \ge 4$. We find that island $I$ emerges at late time and saves entropy bound. And boundary of island $\partial I$ depends on the position of cutoff surface. When cutoff surface is far from horizon, $\partial I$ is inside and near horizon. When cutoff surface is set to be near horizon, $\partial I$ is outside and near horizon. This is different from the case of eternal black hole in which $\partial I$ is always outside horizon no matter cutoff surface is far from or near horizon. We will see that different states will manifestly affect $S_{\text{ent}}$ in island formula when cutoff surface is far from horizon and thus have different result for Page time., Comment: v1:22 pages, 2 figures,v2: typos corrected, an appendix on s-wave approximation is added, references added, published version

In this work we focus on a toy model: (3+1)-dimensional Ho\v{r}ava-Lifshitz gravity coupling with an anisotropic electromagnetic (EM) field which is generated through a Kaluza-Klein reduction of a (4+1)-dimensional Ho\v{r}ava-Lifshitz gravity. This model exhibits a remarkable feature that it has the same velocity for both gravitational and electromagnetic waves. This feature makes it possible to restrict the parameters of the theory from GRB 170817A. In this work we use this feature to discuss possible constraints on the parameter $\beta$ in the theory, by analyzing the possible Lorentz invariance violation effect of the GRB 170817A. This is achieved by analyzing potential time delay of gamma-ray photons in this event. It turns out that it places a stringent constraint on this parameter. In the most ideal case, it gives $|1-\sqrt{\beta}|<(10^{-19}-10^{-18})$., Comment: 21 pages, 2 tables. Accepted for publication in EPJC

Using "complexity=action" proposal we study the late time growth rate of holographic complexity for nonlinear charged Lifshitz black hole with a single horizon or two horizons. As a toy model, we consider two kinds of such black holes: nonlinear charged Lifshitz black hole and nonlinear logarithmic charged Lifshitz black hole. We find that for the black hole with two horizons, the action growth bound is satisfied. But for the black hole with a single horizon, whether the Lloyd bound is violated depends on the specific value of dimensionless coupling constants $\beta_{1},\beta_{2}$, spacetime dimension $D$ and dynamical exponent $z$., Comment: 23 pages, 5 figures

There are increasing evidences that quantum information theory has come to play a fundamental role in quantum gravity especially the holography. In this paper, we show some new potential connections between holography and quantum information theory. Particularly, by utilizing the multiflow description of the holographic entanglement of purification (HEoP) defined in relative homology, we obtain several new inequalities of HEoP under a max multiflow configuration. Each inequality derived for HEoP has a corresponding inequality of the holographic entanglement entropy (HEE). This is further confirmed by geometric analysis. In addition, we conjecture that, based on flow considerations, each property of HEE that can be derived from bit threads may have a corresponding property for HEoP that can be derived from bit threads defined in relative homology., Comment: 20 pages, 4 figures; improvements to presentation, references added, and new section added to roughly comment about the entropy cone of HEoP. Accepted for publication in EPJC

The entanglement of purification (EoP), which measures the classical correlations and entanglement of a given mixed state, has been conjectured to be dual to the area of the minimal cross section of the entanglement wedge in holography. Using the surface-state correspondence, we propose a `bit thread' formulation of the EoP. With this formulation, proofs of some known properties of the EoP are performed. Moreover, we show that the quantum advantage of dense code (QAoDC), which reflects the increase in the rate of classical information transmission through quantum channel due to entanglement, also admits a flow interpretation. In this picture, we can prove the monogamy relation of QAoDC with the EoP for tripartite states. We also derive a new lower bound for $S(AB)$ in terms of QAoDC, which is tighter than the one given by the Araki-Lieb inequality., Comment: 21 pages,7 figures; clarifications added; version to be published in JHEP