A bstract 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 $\mathcal{O}$ 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 function of the scale dimension of $\mathcal{O}$ O and the temperature of each black hole. We argue that the one-sided bulk reconstruction can access the interior region of the black hole.A bstract 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 $$ \mathcal{O} $$ 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 function of the scale dimension of $$ \mathcal{O} $$ O and the temperature of each black hole. We argue that the one-sided bulk reconstruction can access the interior region of the black hole.

arXiv:1807.03916Journal of High Energy PhysicsFeb 1, 2019108 citations

Information radiation in BCFT models of black holes

Moshe Rozali A, James Sully, Mark Van Raamsdonk B +2 more

Abstract In this note, following [1–3], we introduce and study various holographic systems which can describe evaporating black holes. The systems we consider are boundary conformal field theories for which the number of local degrees of freedom on the boundary (cbdy) is large compared to the number of local degrees of freedom in the bulk CFT (cbulk). We consider states where the boundary degrees of freedom on their own would describe an equilibrium black hole, but the coupling to the bulk CFT degrees of freedom allows this black hole to evaporate. The Page time for the black hole is controlled by the ratio cbdy/cbulk. Using both holographic calculations and direct CFT calculations, we study the evolution of the entanglement entropy for the subset of the radiation system (i.e. the bulk CFT) at a distance d > a from the boundary. We find that the entanglement entropy for this subsystem increases until time a + tPage and then undergoes a phase transition after which the entanglement wedge of the radiation system includes the black hole interior. Remarkably, this occurs even if the radiation system is initially at the same temperature as the black hole so that the two are in thermal equilibrium. In this case, even though the black hole does not lose energy, it “radiates” information through interaction with the radiation system until the radiation system contains enough information to reconstruct the black hole interior.Abstract In this note, following [1–3], we introduce and study various holographic systems which can describe evaporating black holes. The systems we consider are boundary conformal field theories for which the number of local degrees of freedom on the boundary (cbdy) is large compared to the number of local degrees of freedom in the bulk CFT (cbulk). We consider states where the boundary degrees of freedom on their own would describe an equilibrium black hole, but the coupling to the bulk CFT degrees of freedom allows this black hole to evaporate. The Page time for the black hole is controlled by the ratio cbdy/cbulk. Using both holographic calculations and direct CFT calculations, we study the evolution of the entanglement entropy for the subset of the radiation system (i.e. the bulk CFT) at a distance d > a from the boundary. We find that the entanglement entropy for this subsystem increases until time a + tPage and then undergoes a phase transition after which the entanglement wedge of the radiation system includes the black hole interior. Remarkably, this occurs even if the radiation system is initially at the same temperature as the black hole so that the two are in thermal equilibrium. In this case, even though the black hole does not lose energy, it “radiates” information through interaction with the radiation system until the radiation system contains enough information to reconstruct the black hole interior.

arXiv:1910.12836Journal of High Energy PhysicsMay 1, 2020194 citations

Entanglement Entropy and Black Hole

Shinji Mukohyama A

Progress of Theoretical Physics SupplementJan 31, 20000 citations

Black hole interiors via spin models

David A. Lowe, Mengyang Tong

To model the interior of a black hole, a study is made of a spin system with long-range random four-spin couplings that exhibits quantum chaos. The black hole limit corresponds to a system where the microstates are approximately degenerate and equally likely, corresponding to the high temperature limit of the spin system. At the leading level of approximation, reconstruction of bulk physics implies that local probes of the black hole should exhibit free propagation and unitary local evolution. We test the conjecture that a particular mean field Hamiltonian provides such a local bulk Hamiltonian by numerically solving the exact Schrodinger equation and comparing the time evolution to the approximate mean field time values. We find excellent agreement between the two time evolutions for timescales smaller than the scrambling time. In earlier work, it was shown bulk evolution along comparable time slices is spoiled by the presence of the curvature singularity, thus the matching found in the present work provides evidence of the success of this approach to interior holography. The numerical solutions also provide a useful testing ground for various measures of quantum chaos and global scrambling. A number of different observables, such as entanglement entropy, out-of-time-order correlators, and trace distance are used to study these effects. This leads to a suitable definition of scrambling time, and evidence is presented showing a logarithmic variation with the system size.To model the interior of a black hole, a study is made of a spin system with long-range random four-spin couplings that exhibits quantum chaos. The black hole limit corresponds to a system where the microstates are approximately degenerate and equally likely, corresponding to the high temperature limit of the spin system. At the leading level of approximation, reconstruction of bulk physics implies that local probes of the black hole should exhibit free propagation and unitary local evolution. We test the conjecture that a particular mean field Hamiltonian provides such a local bulk Hamiltonian by numerically solving the exact Schrodinger equation and comparing the time evolution to the approximate mean field time values. We find excellent agreement between the two time evolutions for timescales smaller than the scrambling time. In earlier work, it was shown bulk evolution along comparable time slices is spoiled by the presence of the curvature singularity, thus the matching found in the present work provides evidence of the success of this approach to interior holography. The numerical solutions also provide a useful testing ground for various measures of quantum chaos and global scrambling. A number of different observables, such as entanglement entropy, out-of-time-order correlators, and trace distance are used to study these effects. This leads to a suitable definition of scrambling time, and evidence is presented showing a logarithmic variation with the system size.

arXiv:1908.11190Physical review. D/Physical review. D.Jul 8, 20201 citation

Power-law corrections to entanglement entropy of black holes

Saurya Das, S. Shankaranarayanan, Sourav Sur

May 15, 20078 citations

\mathcal{O}

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 function of the scale dimension of

\mathcal{O}

O and the temperature of each black hole. We argue that the one-sided bulk reconstruction can access the interior region of the black hole.