Making near-extremal wormholes traversable

Seamus Fallows,Simon F Ross

doi:10.1007/jhep12(2020)044

Abstract

We construct a traversable wormhole from a charged AdS black hole by adding a coupling between the two boundary theories. We investigate how the effect of this deformation behaves in the extremal limit of the black hole. The black holes have finite entropy but an infinitely long throat in the extremal limit. We argue that it is still possible to make the throat traversable even in the extremal limit, but this requires either tuning the field for which we add a boundary coupling close to an instability threshold or scaling the strength of the coupling inversely with the temperature. In the latter case we show that the amount of information that can be sent through the wormhole scales with the entropy.

Highlights

JHEP12(2020)044 infinite wormhole traversable, enabling communication between the two CFTs through the bulk
The divergence in the length of the throat implies that the correlation functions of operators on different boundaries vanishes in the extremal limit, unless the field dual to the operator is tuned to the threshold of an instability [7], suggesting that the effect of the boundary coupling on the bulk geometry may vanish in this limit
We find that unless we tune the bulk field to this instability threshold, we need to take the coupling between the two boundaries to scale to infinity as an inverse power of the temperature to have a finite effect on the bulk geometry in the extremal limit

Summary

Bulk geometry and boundary CFT

2.1 RNAdS bulk solution We consider Einstein-Maxwell gravity with a negative cosmological constant. |ψ = √1 e−β(Ei+μQi)/2|Ei, Qi 1 ⊗ |Ei, −Qi 2 This is a state in the Hilbert space of two copies of the CFT, |ψ ∈ H1⊗H2, corresponding to the two asymptotic boundaries in the full spacetime, where |Ei, Qi are a basis of eigenstates of the Hamiltonian and the U(1) charge in the CFT Hilbert space. For this state to be well-defined at low temperatures, β → ∞, E + μQ must be bounded below. The black hole is the dominant saddle-point in the grand canonical ensemble for all temperatures if μ > μc [16], so it provides the dual of this generalised TFD state. The finite entropy of the black hole in the extremal, zero-temperature limit implies an approximate degeneracy in the states at minimal E + μQ; in the extremal limit the TFD state remains entangled, with an entanglement entropy given by the black hole entropy

Near horizon geometry

Wormhole construction

Charged scalar in AdS2

Calculation of the stress tensor on the horizon

Back-reaction and information bound