We consider a class of pure black hole microstates and demonstrate that they can be made escapable by turning on certain double trace deformations in the CFT. These microstates are dual to BCFT states prepared via a Euclidean path integral starting from a boundary in Euclidean time. These states are dual to black holes in the bulk with an End-of-the-World brane; a codimension one timelike boundary of the spacetime behind the horizon. We show that by tuning the sign of the coupling of the double trace operator to the boundary conditions on the brane the deformation injects negative energy into the black hole causing a time advance for signals behind the horizon. We demonstrate how the property of escapability in the considered microstates follows immediately from the traversability of deformed wormholes. We briefly comment on reconstruction of the black hole interior and state dependence.
The quantum error correction interpretation of AdS/CFT establishes a sense of fluidity to the bulk/boundary dictionary. We show how this property can be utilized to construct a dictionary for operators behind horizons of pure black holes. We demonstrate this within the context of the SYK model with pure black hole microstates obtained via projecting out a single side of the thermofield double (and perturbed versions thereof). Assuming an erasure subsystem code for the duality between the eternal black hole and the thermofield double, this projection results in a rewiring of the dictionary so a…
Different approaches to quantum gravity conclude that black holes may possess an inner horizon, in addition to the (quantum corrected) outer `Schwarzschild' horizon. In this paper we assume the existence of this inner horizon and explain the physical process that might lead to the tunneling of particles through it. It is shown that the tunneling would produce a flux of particles with a spectrum that deviates from the pure thermal one. Under the appropriate approximation the extremely high temperature of this horizon is calculated for an improved quantum black hole. It is argued that the flux o…
We obtain the Buchdahl compactness limit for a pure Lovelock static fluid star and verify that the limit following from the uniform density Schwarzschild's interior solution, which is universal irrespective of the gravitational theory (Einstein or Lovelock), is true in general. In terms of surface potential $Φ(r)$, it means at the surface of the star $r=r_{0}$, $Φ(r_{0}) < 2N(d-N-1)/(d-1)^2$ where $d$, $N$ respectively indicate spacetime dimensions and Lovelock order. For a given $N$, $Φ(r_{0})$ is maximum for $d=2N+2$ while it is always $4/9$, Buchdahl's limit, for $d=3N+1$. It is also remark…
Interior evolution of regular Schwarzschild black holes
Research Centre for Theoretical Physics and Astrophysics, Institute of Physics, Silesian University in Opava（奥帕瓦西里西亚大学物理研究所理论与天体物理研究中心）；Universidad de Tarapacá（塔拉帕卡大学）
We argue that the region behind the horizon of a one-sided black hole can be probed by an analogue of the double-trace deformation protocol of Gao-Jafferis-Wall. This is achieved via a deformation of the CFT Hamiltonian by a term of the form ${\cal O} \widetilde{\cal O}$, where $\widetilde{\cal O}$ denote the state-dependent "mirror operators". We argue that this deformation creates negative energy shockwaves in the bulk, which allow particles inside the horizon to escape and to get directly detected in the CFT. This provides evidence for the smoothness of the horizon of black holes dual to ty…
If a black hole (BH) is initially in an approximately pure state and it evaporates by a unitary process, then the emitted radiation will be in a highly quantum state. As the purifier of this radiation, the state of the BH interior must also be in some highly quantum state. So that, within the interior region, the mean-field approximation cannot be valid and the state of the BH cannot be described by some semiclassical metric. On this basis, we model the state of the BH interior as a collection of a large number of excitations that are packed into closely spaced but single-occupancy energy leve…
We compute the time-dependent entanglement entropy of a CFT which starts in relatively simple initial states. The initial states are the thermofield double for thermal states, dual to eternal black holes, and a particular pure state, dual to a black hole formed by gravitational collapse. The entanglement entropy grows linearly in time. This linear growth is directly related to the growth of the black hole interior measured along "nice" spatial slices. These nice slices probe the spacelike direction in the interior, at a fixed special value of the interior time. In the case of a two-dimensional…
We consider a class of non-equilibrium pure states, which are generally present in an isolated quantum statistical system. These are states of the form $|Ψ\rangle=e^{-{βH \over 2}} U e^{βH \over 2} |Ψ_0\rangle$, where $U$ is a unitary made out of simple operators and $|Ψ_0\rangle$ is a typical equilibrium pure state with sharply peaked energy. We argue that in a system with a holographic dual these states have a natural interpretation as an AdS black hole with transient excitations behind the horizon. We explore the interpretation of these states as pure states undergoing a time-dependent spon…
We introduce a family of partially entangled thermal states in the SYK model that interpolates between the thermo-field double state and a pure (product) state. The states are prepared by a euclidean path integral describing the evolution over two euclidean time segments separated by a local scaling operator $\mathcal{O}$. We argue that the holographic dual of this class of states consists of two black holes with their interior regions connected via a domain wall, described by the worldline of a massive particle. We compute the size of the interior region and the entanglement entropy as a func…
A mechanism capable to provide a natural solution to two major cosmological problems, i.e. the cosmic acceleration and the coincidence problem, is proposed. A specific brane-bulk energy exchange mechanism produces a total dark pressure, arising when adding all normal to the brane negative pressures in the interior of galactic core black holes. This astrophysically produced negative dark pressure explains cosmic acceleration and why the dark energy today is of the same order to the matter density for a wide range of the involved parameters. An exciting result of the analysis is that the recent …
In this note I elaborate on some features of a recent proposal of Papadodimas and Raju for a CFT description of the interior of a one-sided AdS black hole in a pure state. I clarify the treatment of 1/N corrections, and explain how the proposal is able to avoid some of the pitfalls that have disrupted other recent ideas. I argue however that the proposal has the uncomfortable property that states in the CFT Hilbert space do not have definite physical interpretations, unlike in ordinary quantum mechanics. I also contrast the "state-dependence" of the proposal with more familiar phenomena, argui…
The constant density interior Schwarzschild solution for a static, spherically symmetric collapsed star has a divergent pressure when its radius $R\le\frac{9}{8}R_s=\frac{9}{4}GM$. We show that this divergence is integrable, and induces a non-isotropic transverse stress with a finite redshifted surface tension on a spherical surface of radius $R_0=3R\sqrt{1-\frac{8}{9}\frac{R}{R_s}}$. For $r < R_0$ the interior Schwarzschild solution exhibits negative pressure. When $R=R_s$, the surface is localized at the Schwarzschild radius itself, $R_0=R_s$, and the solution has constant negative pressure …
We present a new method for reconstructing CFT duals of states excited by the bulk local operators in the three dimensional AdS black holes in the AdS/CFT context. As an important procedure for this, we introduce a map between the bulk points in AdS and those on the boundary where CFT lives. This gives a systematic and universal way to express bulk local states even inside black hole interiors. Our construction allows us to probe the interior structures of black holes purely from the CFT calculations. We analyze bulk local states in the single-sided black holes as well as the double-sided blac…
The firewall paradox is often presented as arising from double entanglement, but I argue that more generally the paradox is double purity. Near-horizon modes are purified by the interior, in the infalling vacuum. Hence they cannot also be pure alone, or in combination with any third system, as demanded by unitarity. This conflict arises independently of the Page time, for entangled and for pure states. It implies that identifications of Hilbert spaces cannot resolve the paradox. Traditional complementarity requires the unitary identification of infalling matter with a scrambled subsystem of th…
We observe that the entanglement entropy resulting from tracing over a subregion of an initially pure state can grow faster than the surface area of the subregion (indeed, proportional to the volume), in contrast to examples studied previously. The pure states with this property have long-range correlations between interior and exterior modes and are constructed by purification of the desired density matrix. We show that imposing a no-gravitational collapse condition on the pure state is sufficient to exclude faster than area law entropy scaling. This observation leads to an interpretation of …
If one attempts to add momentum-carrying waves to a black string then the solution develops a singularity at the horizon; this is a manifestation of the 'no hair theorem' for black objects. However individual microstates of a black string do not have a horizon, and so the above theorem does not apply. We construct a perturbation that adds momentum to a family of microstates of the extremal D1-D5 string. This perturbation is analogous to the 'singleton' mode localized at the boundary of AdS; to leading order it is pure gauge in the AdS interior of the geometry.
Leinweber Institute for Theoretical Physics, University of California, Berkeley（莱因韦伯理论物理研究所，加州大学伯克利分校）；Martin Fisher School of Physics, Brandeis University（马丁·费舍尔物理学院，布兰迪斯大学）；Department of Physics and Astronomy, University of British Columbia（不列颠哥伦比亚大学物理与天文学系）
We consider the construction of local bulk operators in a black hole background dual to a pure state in conformal field theory. The properties of these operators in a microcanonical ensemble are studied. It has been argued in the literature that typical states in such an ensemble contain firewalls, or otherwise singular horizons. We argue this conclusion can be avoided with a proper definition of the interior operators.
Extending our previous analysis, we study the interior of a Schwarzschild black hole derived from a partial gauge fixing of the full Loop Quantum Gravity Hilbert space, this time including the inverse volume and coherent state subleading corrections. Our derived effective Hamiltonian differs crucially from the ones introduced in the minisuperspace models. This distinction is reflected in the class of homogeneous bouncing geometries that replace the classical singularity and are labeled by a set of quantum parameters associated with the structure of coherent states used to derive the effective …
We study various aspects of the mass deformed SYK model which can escape the interiors of pure boundary state black holes. SYK boundary states are given by a simple local boundary condition on the Majorana fermions and then evolved in Euclidean time in the SYK Hamiltonian. We study the ground state of this mass deformed SYK model in detail. We also use SYK boundary states as a variational approximation to the ground state of the mass deformed SYK model. We compare variational approximation with the exact ground state results and they showed a good agreement. We also study the time evolution of…
