This paper proposes a dual non-perturbative description for maximally extended Schwarzschild Anti-de-Sitter (AdS) spacetimes using two copies of the conformal field theory (CFT) associated with AdS and an initial entangled state. The spacetime is described by an eternal black hole with two asymptotically AdS regions, each viewing the other as behind the horizon. The spacetime is time-dependent and contains spacelike singularities. The holographic description involves two copies of the CFT and an entangled state, which naturally describes the interior of black holes, including near singularities. This approach resolves the initial and final singularities.
The paper discusses the information loss paradox in the context of the eternal black hole spacetime. A calculation shows information loss, but summing over geometries preserves information. The correspondence between the eternal black hole and the CFT is based on Israel's description and is further supported by previous work in AdS/CFT. The eternal black hole is related to an entangled state in the CFT, and black hole entropy is connected to entanglement entropy.
The paper also explores the implications of the holographic description for quantum field theory in the AdS spacetime. It discusses the construction of the Hartle-Hawking-Israel wavefunction, which is a pure state in the CFT. The wavefunction is derived by gluing half the Euclidean geometry to the Lorentzian geometry. The wavefunction is invariant under the difference of the two CFT Hilbert spaces and is used to compute correlation functions for operators inserted on different boundaries.
The paper also discusses the creation of particles in the interior of the AdS-Schwarzschild spacetime by inserting operators on the boundary. The wavefunction for these particles is shown to have positive frequency in the Hartle-Hawking sense. The paper also considers the case of black holes with angular momentum along the $\phi$ circle, which are dual to the same two copies of the CFT but with a different entangled state.
The paper concludes that the eternal black hole spacetime can be described by the CFT with an entangled state, and that the sum over geometries in the Euclidean theory restores unitarity. The paper also discusses the implications of this for the information loss paradox and the possibility of solving it through string theory. The paper emphasizes the importance of the holographic principle in understanding the interior of black holes and the resolution of singularities.This paper proposes a dual non-perturbative description for maximally extended Schwarzschild Anti-de-Sitter (AdS) spacetimes using two copies of the conformal field theory (CFT) associated with AdS and an initial entangled state. The spacetime is described by an eternal black hole with two asymptotically AdS regions, each viewing the other as behind the horizon. The spacetime is time-dependent and contains spacelike singularities. The holographic description involves two copies of the CFT and an entangled state, which naturally describes the interior of black holes, including near singularities. This approach resolves the initial and final singularities.
The paper discusses the information loss paradox in the context of the eternal black hole spacetime. A calculation shows information loss, but summing over geometries preserves information. The correspondence between the eternal black hole and the CFT is based on Israel's description and is further supported by previous work in AdS/CFT. The eternal black hole is related to an entangled state in the CFT, and black hole entropy is connected to entanglement entropy.
The paper also explores the implications of the holographic description for quantum field theory in the AdS spacetime. It discusses the construction of the Hartle-Hawking-Israel wavefunction, which is a pure state in the CFT. The wavefunction is derived by gluing half the Euclidean geometry to the Lorentzian geometry. The wavefunction is invariant under the difference of the two CFT Hilbert spaces and is used to compute correlation functions for operators inserted on different boundaries.
The paper also discusses the creation of particles in the interior of the AdS-Schwarzschild spacetime by inserting operators on the boundary. The wavefunction for these particles is shown to have positive frequency in the Hartle-Hawking sense. The paper also considers the case of black holes with angular momentum along the $\phi$ circle, which are dual to the same two copies of the CFT but with a different entangled state.
The paper concludes that the eternal black hole spacetime can be described by the CFT with an entangled state, and that the sum over geometries in the Euclidean theory restores unitarity. The paper also discusses the implications of this for the information loss paradox and the possibility of solving it through string theory. The paper emphasizes the importance of the holographic principle in understanding the interior of black holes and the resolution of singularities.