The ins and outs of black holes in AdS

Rik van Breukelen

Published Jan 1, 2020• 0 citations

Abstract

This work starts by generalizing the traversable wormhole protocol from the thermofield double state black hole to time-shifted thermofield double state black holes and typical pure state black holes. The protocol is dependent on the time-shift and on the state respectively. The traversability of these states is evidence of the smoothness of the black hole horizons of these states. Inspired by these results, we show that the state-dependent construction of the interior of typical state black holes can be simplified using explicit time dependence. This reduces the state dependence to a single parameter.

DOI: 10.13097/archive-ouverte/unige:142254

Related papers

Black hole state dependence as a single parameter

Rik van Breukelen

Abstract It has previously been proposed that the black hole interior of typical state large black holes in AdS can be described using state-dependent operators. We investigate the possibility that the interior can be described by explicit time dependence, which reduces the state-dependence of the interior operators to a single parameter. We also propose to use the natural cone, obtained from Tomita-Takesaki theory, as a candidate construction for the interior operators.

arXiv:1910.00036Journal of High Energy PhysicsApr 1, 20201 citation

A class of non-equilibrium states and the black hole interior

Kyriakos Papadodimas

arXiv:1708.06328Aug 21, 201720 citations

Quantum teleportation through time-shifted AdS wormholes

Rik van Breukelen, Kyriakos Papadodimas

arXiv:1708.09370Journal of High Energy PhysicsAug 1, 201826 citations

On the interior geometry of a typical black hole microstate

Jan De Boer A, Rik van Breukelen, Sagar F. Lokhande +2 more

Jan 1, 201922 citations

On the interior geometry of a typical black hole microstate

Jan De Boer A, Rik van Breukelen, Sagar F. Lokhande +2 more

arXiv:1804.10580Journal of High Energy PhysicsMay 1, 201927 citations

Probing typical black hole microstates

Jan De Boer A, Rik van Breukelen, Sagar F. Lokhande +2 more

arXiv:1901.08527Journal of High Energy PhysicsJan 1, 202030 citations

The ins and outs of black holes in AdS

Rik van Breukelen

Published Jan 1, 2020• 0 citations

Publisher

Abstract

DOI: 10.13097/archive-ouverte/unige:142254

Related papers

Black hole state dependence as a single parameter

Rik van Breukelen

arXiv:1910.00036Journal of High Energy PhysicsApr 1, 20201 citation

A class of non-equilibrium states and the black hole interior

Kyriakos Papadodimas

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 spontaneous fluctuation out of equilibrium. While these states are atypical and the microscopic phases of the wavefunction are correlated with the matrix elements of simple operators, the states are partly disguised as equilibrium states due to cancellations between contributions from different coarse-grained energy bins. These cancellations are guaranteed by the KMS condition of the underlying equilibrium state $|Ψ_0\rangle$ . However, in correlators which include the Hamiltonian $H$ these cancellations are spoiled and the non-equilibrium nature of the state $|Ψ\rangle$ can be detected. We discuss connections with the proposal that local observables behind the horizon are realized as state-dependent operators. The states studied in this paper may be useful for implementing an analogue of the "traversable wormhole" protocol for a 1-sided black hole, which could potentially allow us to extract the excitation from behind the horizon. We include some pedagogical background material.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 spontaneous fluctuation out of equilibrium. While these states are atypical and the microscopic phases of the wavefunction are correlated with the matrix elements of simple operators, the states are partly disguised as equilibrium states due to cancellations between contributions from different coarse-grained energy bins. These cancellations are guaranteed by the KMS condition of the underlying equilibrium state $|Ψ_0\rangle$. However, in correlators which include the Hamiltonian $H$ these cancellations are spoiled and the non-equilibrium nature of the state $|Ψ\rangle$ can be detected. We discuss connections with the proposal that local observables behind the horizon are realized as state-dependent operators. The states studied in this paper may be useful for implementing an analogue of the "traversable wormhole" protocol for a 1-sided black hole, which could potentially allow us to extract the excitation from behind the horizon. We include some pedagogical background material.

arXiv:1708.06328Aug 21, 201720 citations

Quantum teleportation through time-shifted AdS wormholes

Rik van Breukelen, Kyriakos Papadodimas

Abstract Based on the work of Gao-Jafferis-Wall and Maldacena-Stanford-Yang, we observe that the time-shifted thermofield states of two entangled CFTs can be made traversable by an appropriate coupling of the two CFTs, or alternatively by the application of a modified quantum teleportation protocol. This provides evidence for the smoothness of the horizon for a large class of entangled states related to the thermofield by time-translations. The smoothness of these states has some relevance for the firewall paradox and the proposal that some observables in quantum gravity may be state-dependent. We notice that quantum teleportation through these entangled states could be used in a laboratory setup to implement a “time-machine”, which allows the observer to travel far in the future.Abstract Based on the work of Gao-Jafferis-Wall and Maldacena-Stanford-Yang, we observe that the time-shifted thermofield states of two entangled CFTs can be made traversable by an appropriate coupling of the two CFTs, or alternatively by the application of a modified quantum teleportation protocol. This provides evidence for the smoothness of the horizon for a large class of entangled states related to the thermofield by time-translations. The smoothness of these states has some relevance for the firewall paradox and the proposal that some observables in quantum gravity may be state-dependent. We notice that quantum teleportation through these entangled states could be used in a laboratory setup to implement a “time-machine”, which allows the observer to travel far in the future.

arXiv:1708.09370Journal of High Energy PhysicsAug 1, 201826 citations

On the interior geometry of a typical black hole microstate

Jan De Boer A, Rik van Breukelen, Sagar F. Lokhande +2 more

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 O O ˜ $\\mathcal{O}\\tilde{\\mathcal{O}}$ , where O ˜ $\\tilde{\\mathcal{O}}$ 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 typical states. We argue that the mirror operators allow us to perform an analogue of the Hayden-Preskill decoding protocol. Our claims rely on a technical conjecture about the chaotic behavior of out-of-time-order correlators on typical pure states at scrambling time.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 O O ˜ $$ \\mathcal{O}\\tilde{\\mathcal{O}} $$ , where O ˜ $$ \\tilde{\\mathcal{O}} $$ 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 typical states. We argue that the mirror operators allow us to perform an analogue of the Hayden-Preskill decoding protocol. Our claims rely on a technical conjecture about the chaotic behavior of out-of-time-order correlators on typical pure states at scrambling time.

Jan 1, 201922 citations

On the interior geometry of a typical black hole microstate

Jan De Boer A, Rik van Breukelen, Sagar F. Lokhande +2 more

Abstract 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 $\mathcal{O}\tilde{\mathcal{O}}$ O O ˜ , where $\tilde{\mathcal{O}}$ 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 typical states. We argue that the mirror operators allow us to perform an analogue of the Hayden-Preskill decoding protocol. Our claims rely on a technical conjecture about the chaotic behavior of out-of-time-order correlators on typical pure states at scrambling time.Abstract 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 $$ \mathcal{O}\tilde{\mathcal{O}} $$ O O ˜ , where $$ \tilde{\mathcal{O}} $$ 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 typical states. We argue that the mirror operators allow us to perform an analogue of the Hayden-Preskill decoding protocol. Our claims rely on a technical conjecture about the chaotic behavior of out-of-time-order correlators on typical pure states at scrambling time.

arXiv:1804.10580Journal of High Energy PhysicsMay 1, 201927 citations

Probing typical black hole microstates

Jan De Boer A, Rik van Breukelen, Sagar F. Lokhande +2 more

Abstract We investigate the possibility that the geometry dual to a typical AdS black hole microstate corresponds to the extended AdS-Schwarzschild geometry, including a region spacelike to the exterior. We argue that this region can be described by the mirror operators, a set of state-dependent operators in the dual CFT. We probe the geometry of a typical state by considering state-dependent deformations of the CFT Hamiltonian, which have an interpretation as a one-sided analogue of the Gao-Jafferis-Wall traversable wormhole protocol for typical states. We argue that the validity of the conjectured bulk geometry requires that out-of-time-order correlators of simple CFT operators on typical pure states must exhibit the same chaotic effects as thermal correlators at scrambling time. This condition is related to the question of whether the product of operators separated by scrambling time obey the Eigenstate Thermalization Hypothesis. We investigate some of these statements in the SYK model and discuss similarities with state-dependent perturba- tions of pure states in the SYK model previously considered by Kourkoulou and Maldacena. Finally, we discuss how the mirror operators can be used to implement an analogue of the Hayden-Preskill protocol.Abstract We investigate the possibility that the geometry dual to a typical AdS black hole microstate corresponds to the extended AdS-Schwarzschild geometry, including a region spacelike to the exterior. We argue that this region can be described by the mirror operators, a set of state-dependent operators in the dual CFT. We probe the geometry of a typical state by considering state-dependent deformations of the CFT Hamiltonian, which have an interpretation as a one-sided analogue of the Gao-Jafferis-Wall traversable wormhole protocol for typical states. We argue that the validity of the conjectured bulk geometry requires that out-of-time-order correlators of simple CFT operators on typical pure states must exhibit the same chaotic effects as thermal correlators at scrambling time. This condition is related to the question of whether the product of operators separated by scrambling time obey the Eigenstate Thermalization Hypothesis. We investigate some of these statements in the SYK model and discuss similarities with state-dependent perturba- tions of pure states in the SYK model previously considered by Kourkoulou and Maldacena. Finally, we discuss how the mirror operators can be used to implement an analogue of the Hayden-Preskill protocol.

arXiv:1901.08527Journal of High Energy PhysicsJan 1, 202030 citations

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 spontaneous fluctuation out of equilibrium. While these states are atypical and the microscopic phases of the wavefunction are correlated with the matrix elements of simple operators, the states are partly disguised as equilibrium states due to cancellations between contributions from different coarse-grained energy bins. These cancellations are guaranteed by the KMS condition of the underlying equilibrium state

|Ψ_0\rangle

. However, in correlators which include the Hamiltonian

H

these cancellations are spoiled and the non-equilibrium nature of the state

|Ψ\rangle

can be detected. We discuss connections with the proposal that local observables behind the horizon are realized as state-dependent operators. The states studied in this paper may be useful for implementing an analogue of the "traversable wormhole" protocol for a 1-sided black hole, which could potentially allow us to extract the excitation from behind the horizon. We include some pedagogical background material.

\\mathcal{O}\\tilde{\\mathcal{O}}

, where O ˜

\\tilde{\\mathcal{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 typical states. We argue that the mirror operators allow us to perform an analogue of the Hayden-Preskill decoding protocol. Our claims rely on a technical conjecture about the chaotic behavior of out-of-time-order correlators on typical pure states at scrambling time.

\mathcal{O}\tilde{\mathcal{O}}

O O ˜ , where

\tilde{\mathcal{O}}

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 typical states. We argue that the mirror operators allow us to perform an analogue of the Hayden-Preskill decoding protocol. Our claims rely on a technical conjecture about the chaotic behavior of out-of-time-order correlators on typical pure states at scrambling time.