Evaporating universes

Abstract

Recent work by Headrick, Sasieta and myself provides an extension of the HRT formula for asymptotically flat spacetimes. I use this formula to construct a holographic model of black hole evaporation in four-dimensional asymptotically flat spacetimes using Brill-Lindquist (BL) wormholes. The wormhole is interpreted via ER=EPR to represent the entanglement geometry between an evaporating black hole and baths into which the Hawking radiation is collected. Applying HRT, I compute the entanglement entropy by numerically computing the areas of the minimal surfaces, which is shown to obey the Page curve, consistent with information conservation. Numerical analysis is done for both three and four-boundary BL wormholes ($n=3,4$). Index-1 surfaces in the wormhole interior are interpreted as the candidate bulges involved in the python's lunch conjecture (PLC), and their areas are used to compute the restricted complexity $\mathcal{C}$ of decoding the Hawking radiation. The results are compared to the time-dependent predictions of the PLC.

Figures (26)

• Figure 1: Quantum octopus for an evaporating black hole. Though the radiation and black hole exist in the same connected region, we take them to be sufficiently far apart such that they are approximated to be living on disconnected sheets (as in a wormhole). Reproduced from erEpr.
• Figure 2: Entanglement wormhole structure in Akers:2019nfi. With time, more black holes are emitted and entangled to the existing 'octopus' geometry, which grows $n$ legs. Reproduced from Akers:2019nfi.
• Figure 3: Embedding diagram of BL initial data geometry for $n=3$, $\alpha_1=\alpha_2=:\alpha$, and large separation, $\|\vec{r}_1-\vec{r}_2\|\gg \alpha$. There are two Einstein-Rosen bridges and two minimal surfaces $\gamma_1$, $\gamma_2$. Adapted from brill-lindquist.
• Figure 4: Embedding diagram of BL initial data geometry for small separation, $r_{12}\ll \alpha$. Adapted from brill-lindquist.
• Figure 5: Planar sections of minimal surfaces $\gamma_{1,2,3}$ (solid curves) and index-1 extremal surfaces $\tilde{\gamma}_{1,2,3}$ (dashed curves) in (left) original $\vec{r}$ coordinates and (right) inverted $\vec{s}$ coordinates