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.
Highlights
Using both holographic calculations and direct conformal field theories (CFTs) calculations, we study the evolution of the entanglement entropy for the subset of the radiation system at a distance d > a from the boundary
We find that the entanglement entropy for this subsystem increases until time a + tPage and undergoes a phase transition after which the entanglement wedge of the radiation system includes the black hole interior
A fascinating suggestion [12] to avoid this firewall conclusion, making use of the general idea that the connectivity of spacetime is related to quantum entanglement between underlying degrees of freedom [13, 14], is that the entanglement between the black hole and its early radiation past the Page time is responsible for the existence of a smooth geometry behind the black hole horizon, in the same way that the entanglement between two conformal field theories (CFTs) in the thermofield double state gives rise to a smooth wormhole geometry connecting the two black hole exteriors
Summary
A schematic of our basic setup is shown in figure 1A. We imagine starting with a holographic system on Sd−1 whose high-energy states or high-temperature thermal states describe black holes in a dual gravitational picture. We have in mind that cbdy cbulk 1 This will allow the full system to be holographic, but as we show below, will give a parametrically large evaporation time. For a boundary system of size R. for a boundary system of size R If this system is coupled to a higher-dimensional CFT with cbulk local degrees of freedom, we expect that the energy will be radiated away at a rate dE dt. The Page time is when half the (macroscopic) entropy of the black hole has been radiated We can compare this to the calculation in [29] of Page (see [34]), who considers perfectly absorbing boundary conditions for a large black hole in AdS Using those results, one finds a Page time. In order that the full system is holographic, we want to take cbdy cbulk 1
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
