Cool horizons for entangled black holes

TL;DR

<3-5 sentence high-level summary>

Abstract

General relativity contains solutions in which two distant black holes are connected through the interior via a wormhole, or Einstein-Rosen bridge. These solutions can be interpreted as maximally entangled states of two black holes that form a complex EPR pair. We suggest that similar bridges might be present for more general entangled states. In the case of entangled black holes one can formulate versions of the AMPS(S) paradoxes and resolve them. This suggests possible resolutions of the firewall paradoxes for more general situations.

Figures (22)

• Figure 1: Penrose diagram of the eternal black hole in $AdS$. 1 and 2, or Left and Right, denote the two boundaries and the two CFT's that the system is dual to.
• Figure 2: Maximally extended Schwarzschild spacetime. There are two asymptotic regions. The blue spatial slice contains the Einstein-Rosen bridge connecting the two regions.
• Figure 3: (a) Another representation of the blue spatial slice of figure \ref{['2']}. It contains a neck connecting two asymptotically flat regions. (b) Here we have two distant entangled black holes in the same space. The horizons are identified as indicated. This is not an exact solution of the equations but an approximate solution where we can ignore the small force between the black holes.
• Figure 4: (a) Picture of the Euclidean instanton describing the creation of a black hole pair in a magnetic field. The space consists of two pieces joined along a cylinder with the topology $S^1 \times S^2$. The $S^1$ is the circle drawn here. The bottom "cup" represents an approximately $H_2 \times S^2$ geometry which is the near horizon geometry of the extremal black holes. Despite appearances the distance through the $H_2$ section is shorter than through the plane. (b) Lorentzian continuation across $t=0$ gives a pair of accelerating black holes.
• Figure 5: (a) The yellow shaded region corresponds to the Einstein Rosen bridge associated to the entangled state $|\Psi_{t=0}\rangle$ in (\ref{['familyt']}) (for an $AdS_3/CFT_2$ situation). One can draw different spatial sections in the geometry. The physics in these slices is related by the bulk Wheeler deWitt equation. (b) Here we see the bridge corresponding to the entangled state $|\Psi_t\rangle$, for $r>0$. (c) This is a different presentation of the same bridge as in (b), related by the action of a boost $H_R - H_L$. Even though the states (a) and $(c)$ are different, they both contain regions $A$ and $B$ which look the same.